[{"article_type":"original","file_date_updated":"2024-07-16T10:35:10Z","language":[{"iso":"eng"}],"doi":"10.1112/blms.12965","oa_version":"Published Version","scopus_import":"1","_id":"14660","quality_controlled":"1","date_created":"2023-12-10T23:00:58Z","isi":1,"publisher":"London Mathematical Society","year":"2024","publication_status":"published","department":[{"_id":"UlWa"}],"type":"journal_article","oa":1,"day":"01","external_id":{"isi":["001113277100001"],"arxiv":["2212.04308"]},"title":"Quantitative Steinitz theorem: A polynomial bound","article_processing_charge":"Yes (via OA deal)","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"arxiv":1,"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2024-02-01T00:00:00Z","corr_author":"1","has_accepted_license":"1","abstract":[{"lang":"eng","text":"The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set 𝑆⊂ℝ𝑑, then there are at most 2𝑑 points of 𝑆 whose convex hull contains the origin in the interior. Bárány, Katchalski,and Pach proved the following quantitative version of Steinitz’s theorem. Let 𝑄 be a convex polytope in ℝ𝑑 containing the standard Euclidean unit ball 𝐁𝑑. Then there exist at most 2𝑑 vertices of 𝑄 whose convex hull 𝑄′ satisfies 𝑟𝐁𝑑⊂𝑄′ with 𝑟⩾𝑑−2𝑑. They conjectured that 𝑟⩾𝑐𝑑−1∕2 holds with a universal constant 𝑐>0. We prove 𝑟⩾15𝑑2, the first polynomial lower bound on 𝑟. Furthermore, we show that 𝑟 is not greater than 2/√𝑑."}],"citation":{"ista":"Ivanov G, Naszódi M. 2024. Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society. 56(2), 796–802.","chicago":"Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A Polynomial Bound.” <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society, 2024. <a href=\"https://doi.org/10.1112/blms.12965\">https://doi.org/10.1112/blms.12965</a>.","ama":"Ivanov G, Naszódi M. Quantitative Steinitz theorem: A polynomial bound. <i>Bulletin of the London Mathematical Society</i>. 2024;56(2):796-802. doi:<a href=\"https://doi.org/10.1112/blms.12965\">10.1112/blms.12965</a>","apa":"Ivanov, G., &#38; Naszódi, M. (2024). Quantitative Steinitz theorem: A polynomial bound. <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/blms.12965\">https://doi.org/10.1112/blms.12965</a>","mla":"Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A Polynomial Bound.” <i>Bulletin of the London Mathematical Society</i>, vol. 56, no. 2, London Mathematical Society, 2024, pp. 796–802, doi:<a href=\"https://doi.org/10.1112/blms.12965\">10.1112/blms.12965</a>.","ieee":"G. Ivanov and M. Naszódi, “Quantitative Steinitz theorem: A polynomial bound,” <i>Bulletin of the London Mathematical Society</i>, vol. 56, no. 2. London Mathematical Society, pp. 796–802, 2024.","short":"G. Ivanov, M. Naszódi, Bulletin of the London Mathematical Society 56 (2024) 796–802."},"intvolume":"        56","date_updated":"2025-09-04T11:31:49Z","author":[{"last_name":"Ivanov","first_name":"Grigory","full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E"},{"full_name":"Naszódi, Márton","last_name":"Naszódi","first_name":"Márton"}],"status":"public","issue":"2","publication":"Bulletin of the London Mathematical Society","ddc":["510"],"volume":56,"acknowledgement":"M.N. was supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences aswell as the National Research, Development and Innovation Fund (NRDI) grants K119670 andK131529, and the ÚNKP-22-5 New National Excellence Program of the Ministry for Innovationand Technology from the source of the NRDI as well as the ELTE TKP 2021-NKTA-62 fundingscheme","month":"02","page":"796-802","file":[{"creator":"dernst","date_updated":"2024-07-16T10:35:10Z","date_created":"2024-07-16T10:35:10Z","access_level":"open_access","relation":"main_file","checksum":"30ea0694757bc668cf7cd15ae357b35e","success":1,"file_name":"2024_BulletinLondonMathSoc_Ivanov.pdf","file_id":"17259","file_size":111756,"content_type":"application/pdf"}]},{"month":"08","ddc":["512"],"ec_funded":1,"volume":56,"acknowledgement":"We thank Oleksiy Klurman, Ilya Shkredov, and Igor Shparlinski for helpful comments on earlier versions of the paper, and thank Yotam Hendel for providing a reference for Lemma 2.1. We also thank the anonymous referee for their generous corrections and comments. The first author has received funding from the European Union's Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie Grant Agreement Number: 101034413. The second author is partially supported by the Cuthbert C. Hurd Graduate Fellowship in the Mathematical Sciences, Stanford.","file":[{"date_updated":"2024-08-20T08:36:32Z","creator":"vwang","date_created":"2024-08-20T08:36:32Z","access_level":"open_access","relation":"main_file","checksum":"ae386a4031856efac23c7cdcb53b559b","file_name":"Paucity_phenomena_for_polynomial_products__Wang_Xu_ (7).pdf","success":1,"file_id":"17446","file_size":331775,"content_type":"application/pdf"}],"page":"2718-2726","author":[{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","full_name":"Wang, Victor","last_name":"Wang","orcid":"0000-0002-0704-7026","first_name":"Victor"},{"last_name":"Xu","first_name":"Max Wenqiang","full_name":"Xu, Max Wenqiang"}],"status":"public","issue":"8","publication":"Bulletin of the London Mathematical Society","intvolume":"        56","date_updated":"2025-09-08T08:57:32Z","date_published":"2024-08-01T00:00:00Z","citation":{"ama":"Wang V, Xu MW. Paucity phenomena for polynomial products. <i>Bulletin of the London Mathematical Society</i>. 2024;56(8):2718-2726. doi:<a href=\"https://doi.org/10.1112/blms.13095\">10.1112/blms.13095</a>","chicago":"Wang, Victor, and Max Wenqiang Xu. “Paucity Phenomena for Polynomial Products.” <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society, 2024. <a href=\"https://doi.org/10.1112/blms.13095\">https://doi.org/10.1112/blms.13095</a>.","short":"V. Wang, M.W. Xu, Bulletin of the London Mathematical Society 56 (2024) 2718–2726.","ieee":"V. Wang and M. W. Xu, “Paucity phenomena for polynomial products,” <i>Bulletin of the London Mathematical Society</i>, vol. 56, no. 8. London Mathematical Society, pp. 2718–2726, 2024.","mla":"Wang, Victor, and Max Wenqiang Xu. “Paucity Phenomena for Polynomial Products.” <i>Bulletin of the London Mathematical Society</i>, vol. 56, no. 8, London Mathematical Society, 2024, pp. 2718–26, doi:<a href=\"https://doi.org/10.1112/blms.13095\">10.1112/blms.13095</a>.","apa":"Wang, V., &#38; Xu, M. W. (2024). Paucity phenomena for polynomial products. <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/blms.13095\">https://doi.org/10.1112/blms.13095</a>","ista":"Wang V, Xu MW. 2024. Paucity phenomena for polynomial products. Bulletin of the London Mathematical Society. 56(8), 2718–2726."},"abstract":[{"lang":"eng","text":"Let  P(x)∈Z[x] be a polynomial with at least two distinct complex roots. We prove that the number of solutions  (x1,…,xk,y1,…,yk)∈[N]2k to the equation\r\n∏1≤i≤kP(xi)=∏1≤j≤kP(yj)≠0\r\n(for any  k≥1 ) is asymptotically  k!Nk  as  N→+∞. This solves a question first proposed and studied by Najnudel. The result can also be interpreted as saying that all even moments of random partial sums  1N√∑n≤Nf(P(n)) match standard complex Gaussian moments as  N→+∞\r\n , where  f is the Steinhaus random multiplicative function."}],"has_accepted_license":"1","title":"Paucity phenomena for polynomial products","article_processing_charge":"No","arxiv":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_identifier":{"eissn":["1469-2120"],"issn":["0024-6093"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2211.02908","open_access":"1"}],"department":[{"_id":"TiBr"}],"publisher":"London Mathematical Society","publication_status":"published","year":"2024","oa":1,"day":"01","external_id":{"isi":["001235729900001"],"arxiv":["2211.02908"]},"type":"journal_article","quality_controlled":"1","project":[{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413"}],"isi":1,"date_created":"2024-06-09T22:01:03Z","language":[{"iso":"eng"}],"file_date_updated":"2024-08-20T08:36:32Z","article_type":"original","oa_version":"Submitted Version","scopus_import":"1","_id":"17127","doi":"10.1112/blms.13095"},{"author":[{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan","first_name":"Matthew Alan","last_name":"Kwan","orcid":"0000-0002-4003-7567"},{"last_name":"Wigderson","first_name":"Yuval","full_name":"Wigderson, Yuval"}],"status":"public","issue":"10","publication":"Bulletin of the London Mathematical Society","month":"10","ddc":["510"],"volume":56,"acknowledgement":"The authors are grateful to Noga Alon, Anurag Bishnoi, Clive Elphick, and Ferdinand Ihringer for helpful comments and interesting discussions on earlier drafts of this paper. Matthew Kwan is supported by ERC Starting Grant “RANDSTRUCT” No. 101076777. Yuval Wigderson is supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.\r\nOpen access funding provided by Eidgenossische Technische Hochschule Zurich.","file":[{"date_created":"2025-01-09T13:36:53Z","access_level":"open_access","creator":"dernst","date_updated":"2025-01-09T13:36:53Z","checksum":"7117f9819eaeb45eef1b0a226f9c2709","relation":"main_file","file_id":"18814","success":1,"file_name":"2024_BulletinLondonMathSoc_Kwan.pdf","content_type":"application/pdf","file_size":175966}],"page":"3196-3208","date_published":"2024-10-01T00:00:00Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"ista":"Kwan MA, Wigderson Y. 2024. The inertia bound is far from tight. Bulletin of the London Mathematical Society. 56(10), 3196–3208.","apa":"Kwan, M. A., &#38; Wigderson, Y. (2024). The inertia bound is far from tight. <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/blms.13127\">https://doi.org/10.1112/blms.13127</a>","ieee":"M. A. Kwan and Y. Wigderson, “The inertia bound is far from tight,” <i>Bulletin of the London Mathematical Society</i>, vol. 56, no. 10. London Mathematical Society, pp. 3196–3208, 2024.","mla":"Kwan, Matthew Alan, and Yuval Wigderson. “The Inertia Bound Is Far from Tight.” <i>Bulletin of the London Mathematical Society</i>, vol. 56, no. 10, London Mathematical Society, 2024, pp. 3196–208, doi:<a href=\"https://doi.org/10.1112/blms.13127\">10.1112/blms.13127</a>.","short":"M.A. Kwan, Y. Wigderson, Bulletin of the London Mathematical Society 56 (2024) 3196–3208.","chicago":"Kwan, Matthew Alan, and Yuval Wigderson. “The Inertia Bound Is Far from Tight.” <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society, 2024. <a href=\"https://doi.org/10.1112/blms.13127\">https://doi.org/10.1112/blms.13127</a>.","ama":"Kwan MA, Wigderson Y. The inertia bound is far from tight. <i>Bulletin of the London Mathematical Society</i>. 2024;56(10):3196-3208. doi:<a href=\"https://doi.org/10.1112/blms.13127\">10.1112/blms.13127</a>"},"abstract":[{"lang":"eng","text":"The inertia bound and ratio bound (also known as the Cvetković bound and Hoffman bound) are two fundamental inequalities in spectral graph theory, giving upper bounds on the independence number α(G) of a graph G in terms of spectral information about a weighted adjacency matrix of G. For both inequalities, given a graph G, one needs to make a judicious choice of weighted adjacency matrix to obtain as strong a bound as possible.\r\nWhile there is a well-established theory surrounding the ratio bound, the inertia bound is much more mysterious, and its limits are rather unclear. In fact, only recently did Sinkovic find the first example of a graph for which the inertia bound is not tight (for any weighted adjacency matrix), answering a longstanding question of Godsil. We show that the inertia bound can be extremely far from tight, and in fact can significantly underperform the ratio bound: for example, one of our results is that for infinitely many n, there is an n-vertex graph for which even the unweighted ratio bound can prove α(G)≤4n3/4, but the inertia bound is always at least n/4. In particular, these results address questions of Rooney, Sinkovic, and Wocjan--Elphick--Abiad."}],"has_accepted_license":"1","intvolume":"        56","date_updated":"2025-09-08T08:45:39Z","department":[{"_id":"MaKw"}],"publisher":"London Mathematical Society","year":"2024","publication_status":"published","OA_type":"hybrid","oa":1,"day":"01","external_id":{"arxiv":["2312.04925"],"isi":["001279563300001"]},"type":"journal_article","title":"The inertia bound is far from tight","article_processing_charge":"Yes (via OA deal)","arxiv":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"language":[{"iso":"eng"}],"OA_place":"publisher","file_date_updated":"2025-01-09T13:36:53Z","article_type":"original","scopus_import":"1","oa_version":"Published Version","_id":"17376","doi":"10.1112/blms.13127","quality_controlled":"1","project":[{"grant_number":"101076777","name":"Randomness and structure in combinatorics","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"}],"isi":1,"date_created":"2024-08-04T22:01:22Z"},{"license":"https://creativecommons.org/licenses/by-nc/4.0/","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"title":"Large deviations in random latin squares","article_processing_charge":"No","oa":1,"external_id":{"arxiv":["2106.11932"],"isi":["000779920900001"]},"day":"01","type":"journal_article","department":[{"_id":"MaKw"}],"publisher":"Wiley","year":"2022","publication_status":"published","isi":1,"date_created":"2022-04-17T22:01:48Z","quality_controlled":"1","scopus_import":"1","oa_version":"Published Version","_id":"11186","doi":"10.1112/blms.12638","language":[{"iso":"eng"}],"file_date_updated":"2023-02-03T09:43:38Z","article_type":"original","file":[{"relation":"main_file","checksum":"02d74e7ae955ba3c808e2a8aebe6ef98","date_updated":"2023-02-03T09:43:38Z","creator":"dernst","date_created":"2023-02-03T09:43:38Z","access_level":"open_access","file_size":233758,"content_type":"application/pdf","file_name":"2022_BulletinMathSociety_Kwan.pdf","success":1,"file_id":"12499"}],"page":"1420-1438","month":"08","ddc":["510"],"acknowledgement":"We thank Zach Hunter for pointing out some important typographical errors. We also thank the referee for several remarks which helped improve the paper substantially.\r\nKwan was supported by NSF grant DMS-1953990. Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE-1745302.","volume":54,"issue":"4","publication":"Bulletin of the London Mathematical Society","author":[{"first_name":"Matthew Alan","last_name":"Kwan","orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"},{"full_name":"Sah, Ashwin","last_name":"Sah","first_name":"Ashwin"},{"last_name":"Sawhney","first_name":"Mehtaab","full_name":"Sawhney, Mehtaab"}],"status":"public","date_updated":"2024-10-09T21:02:21Z","intvolume":"        54","abstract":[{"lang":"eng","text":"In this note, we study large deviations of the number  𝐍  of intercalates ( 2×2  combinatorial subsquares which are themselves Latin squares) in a random  𝑛×𝑛  Latin square. In particular, for constant  𝛿>0  we prove that  exp(−𝑂(𝑛2log𝑛))⩽Pr(𝐍⩽(1−𝛿)𝑛2/4)⩽exp(−Ω(𝑛2))  and  exp(−𝑂(𝑛4/3(log𝑛)))⩽Pr(𝐍⩾(1+𝛿)𝑛2/4)⩽exp(−Ω(𝑛4/3(log𝑛)2/3)) . As a consequence, we deduce that a typical order- 𝑛  Latin square has  (1+𝑜(1))𝑛2/4  intercalates, matching a lower bound due to Kwan and Sudakov and resolving an old conjecture of McKay and Wanless."}],"citation":{"chicago":"Kwan, Matthew Alan, Ashwin Sah, and Mehtaab Sawhney. “Large Deviations in Random Latin Squares.” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2022. <a href=\"https://doi.org/10.1112/blms.12638\">https://doi.org/10.1112/blms.12638</a>.","ama":"Kwan MA, Sah A, Sawhney M. Large deviations in random latin squares. <i>Bulletin of the London Mathematical Society</i>. 2022;54(4):1420-1438. doi:<a href=\"https://doi.org/10.1112/blms.12638\">10.1112/blms.12638</a>","apa":"Kwan, M. A., Sah, A., &#38; Sawhney, M. (2022). Large deviations in random latin squares. <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/blms.12638\">https://doi.org/10.1112/blms.12638</a>","short":"M.A. Kwan, A. Sah, M. Sawhney, Bulletin of the London Mathematical Society 54 (2022) 1420–1438.","ieee":"M. A. Kwan, A. Sah, and M. Sawhney, “Large deviations in random latin squares,” <i>Bulletin of the London Mathematical Society</i>, vol. 54, no. 4. Wiley, pp. 1420–1438, 2022.","mla":"Kwan, Matthew Alan, et al. “Large Deviations in Random Latin Squares.” <i>Bulletin of the London Mathematical Society</i>, vol. 54, no. 4, Wiley, 2022, pp. 1420–38, doi:<a href=\"https://doi.org/10.1112/blms.12638\">10.1112/blms.12638</a>.","ista":"Kwan MA, Sah A, Sawhney M. 2022. Large deviations in random latin squares. Bulletin of the London Mathematical Society. 54(4), 1420–1438."},"has_accepted_license":"1","corr_author":"1","date_published":"2022-08-01T00:00:00Z","tmp":{"short":"CC BY-NC (4.0)","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","image":"/images/cc_by_nc.png","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode"}},{"citation":{"ama":"Ivanov G. No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. <i>Bulletin of the London Mathematical Society</i>. 2021;53(2):631-641. doi:<a href=\"https://doi.org/10.1112/blms.12449\">10.1112/blms.12449</a>","chicago":"Ivanov, Grigory. “No-Dimension Tverberg’s Theorem and Its Corollaries in Banach Spaces of Type P.” <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society, 2021. <a href=\"https://doi.org/10.1112/blms.12449\">https://doi.org/10.1112/blms.12449</a>.","ieee":"G. Ivanov, “No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p,” <i>Bulletin of the London Mathematical Society</i>, vol. 53, no. 2. London Mathematical Society, pp. 631–641, 2021.","mla":"Ivanov, Grigory. “No-Dimension Tverberg’s Theorem and Its Corollaries in Banach Spaces of Type P.” <i>Bulletin of the London Mathematical Society</i>, vol. 53, no. 2, London Mathematical Society, 2021, pp. 631–41, doi:<a href=\"https://doi.org/10.1112/blms.12449\">10.1112/blms.12449</a>.","short":"G. Ivanov, Bulletin of the London Mathematical Society 53 (2021) 631–641.","apa":"Ivanov, G. (2021). No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/blms.12449\">https://doi.org/10.1112/blms.12449</a>","ista":"Ivanov G. 2021. No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. Bulletin of the London Mathematical Society. 53(2), 631–641."},"abstract":[{"text":"We continue our study of ‘no‐dimension’ analogues of basic theorems in combinatorial and convex geometry in Banach spaces. We generalize some results of the paper (Adiprasito, Bárány and Mustafa, ‘Theorems of Carathéodory, Helly, and Tverberg without dimension’, Proceedings of the Thirtieth Annual ACM‐SIAM Symposium on Discrete Algorithms (Society for Industrial and Applied Mathematics, San Diego, California, 2019) 2350–2360) and prove no‐dimension versions of the colored Tverberg theorem, the selection lemma and the weak  𝜀 ‐net theorem in Banach spaces of type  𝑝>1 . To prove these results, we use the original ideas of Adiprasito, Bárány and Mustafa for the Euclidean case, our no‐dimension version of the Radon theorem and slightly modified version of the celebrated Maurey lemma.","lang":"eng"}],"has_accepted_license":"1","date_published":"2021-04-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)"},"date_updated":"2025-07-10T12:01:31Z","intvolume":"        53","publication":"Bulletin of the London Mathematical Society","issue":"2","author":[{"full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","first_name":"Grigory","last_name":"Ivanov"}],"status":"public","file":[{"checksum":"e6ceaa6470d835eb4c211cbdd38fdfd1","relation":"main_file","access_level":"open_access","date_created":"2021-08-06T09:59:45Z","creator":"kschuh","date_updated":"2021-08-06T09:59:45Z","content_type":"application/pdf","file_size":194550,"file_id":"9796","success":1,"file_name":"2021_BLMS_Ivanov.pdf"}],"page":"631-641","month":"04","ddc":["510"],"volume":53,"acknowledgement":"I wish to thank Imre Bárány for bringing the problem to my attention. I am grateful to Marton Naszódi and Igor Tsiutsiurupa for useful remarks and help with the text.\r\nThe author acknowledges the financial support from the Ministry of Educational and Science of the Russian Federation in the framework of MegaGrant no 075‐15‐2019‐1926.","oa_version":"Published Version","scopus_import":"1","_id":"9037","doi":"10.1112/blms.12449","file_date_updated":"2021-08-06T09:59:45Z","language":[{"iso":"eng"}],"article_type":"original","isi":1,"date_created":"2021-01-24T23:01:08Z","quality_controlled":"1","oa":1,"day":"01","external_id":{"isi":["000607265100001"],"arxiv":["1912.08561"]},"type":"journal_article","department":[{"_id":"UlWa"}],"publisher":"London Mathematical Society","publication_status":"published","year":"2021","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1469-2120"],"issn":["0024-6093"]},"title":"No-dimension Tverberg's theorem and its corollaries in Banach spaces of type p","article_processing_charge":"Yes (via OA deal)"},{"extern":"1","date_updated":"2023-02-23T14:01:21Z","intvolume":"        53","citation":{"short":"J. Fox, M.A. Kwan, B. Sudakov, Bulletin of the London Mathematical Society 53 (2021) 619–630.","ieee":"J. Fox, M. A. Kwan, and B. Sudakov, “Acyclic subgraphs of tournaments with high chromatic number,” <i>Bulletin of the London Mathematical Society</i>, vol. 53, no. 2. Wiley, pp. 619–630, 2021.","mla":"Fox, Jacob, et al. “Acyclic Subgraphs of Tournaments with High Chromatic Number.” <i>Bulletin of the London Mathematical Society</i>, vol. 53, no. 2, Wiley, 2021, pp. 619–30, doi:<a href=\"https://doi.org/10.1112/blms.12446\">10.1112/blms.12446</a>.","apa":"Fox, J., Kwan, M. A., &#38; Sudakov, B. (2021). Acyclic subgraphs of tournaments with high chromatic number. <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/blms.12446\">https://doi.org/10.1112/blms.12446</a>","ama":"Fox J, Kwan MA, Sudakov B. Acyclic subgraphs of tournaments with high chromatic number. <i>Bulletin of the London Mathematical Society</i>. 2021;53(2):619-630. doi:<a href=\"https://doi.org/10.1112/blms.12446\">10.1112/blms.12446</a>","chicago":"Fox, Jacob, Matthew Alan Kwan, and Benny Sudakov. “Acyclic Subgraphs of Tournaments with High Chromatic Number.” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2021. <a href=\"https://doi.org/10.1112/blms.12446\">https://doi.org/10.1112/blms.12446</a>.","ista":"Fox J, Kwan MA, Sudakov B. 2021. Acyclic subgraphs of tournaments with high chromatic number. Bulletin of the London Mathematical Society. 53(2), 619–630."},"abstract":[{"lang":"eng","text":"We prove that every n-vertex tournament G has an acyclic subgraph with chromatic number at least n5/9−o(1), while there exists an n-vertex tournament G whose every acyclic subgraph has chromatic number at most n3/4+o(1). This establishes in a strong form a conjecture of Nassar and Yuster and improves on another result of theirs. Our proof combines probabilistic and spectral techniques together with some additional ideas. In particular, we prove a lemma showing that every tournament with many transitive subtournaments has a large subtournament that is almost transitive. This may be of independent interest."}],"date_published":"2021-04-03T00:00:00Z","page":"619-630","volume":53,"month":"04","issue":"2","publication":"Bulletin of the London Mathematical Society","author":[{"full_name":"Fox, Jacob","first_name":"Jacob","last_name":"Fox"},{"last_name":"Kwan","orcid":"0000-0002-4003-7567","first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan"},{"full_name":"Sudakov, Benny","first_name":"Benny","last_name":"Sudakov"}],"status":"public","date_created":"2021-06-21T06:11:56Z","quality_controlled":"1","doi":"10.1112/blms.12446","scopus_import":"1","oa_version":"Preprint","_id":"9572","article_type":"original","language":[{"iso":"eng"}],"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","publication_identifier":{"eissn":["1469-2120"],"issn":["0024-6093"]},"arxiv":1,"title":"Acyclic subgraphs of tournaments with high chromatic number","article_processing_charge":"No","type":"journal_article","oa":1,"external_id":{"arxiv":["1912.07722"]},"day":"03","publisher":"Wiley","year":"2021","publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1912.07722","open_access":"1"}]},{"volume":53,"month":"04","page":"560-574","status":"public","author":[{"first_name":"Kamil P","last_name":"Rychlewicz","full_name":"Rychlewicz, Kamil P","id":"85A07246-A8BF-11E9-B4FA-D9E3E5697425"}],"publication":"Bulletin of the London Mathematical Society","issue":"2","intvolume":"        53","date_updated":"2024-10-09T20:59:03Z","date_published":"2021-04-01T00:00:00Z","corr_author":"1","citation":{"ista":"Rychlewicz KP. 2021. The positivity of local equivariant Hirzebruch class for toric varieties. Bulletin of the London Mathematical Society. 53(2), 560–574.","ama":"Rychlewicz KP. The positivity of local equivariant Hirzebruch class for toric varieties. <i>Bulletin of the London Mathematical Society</i>. 2021;53(2):560-574. doi:<a href=\"https://doi.org/10.1112/blms.12442\">10.1112/blms.12442</a>","chicago":"Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class for Toric Varieties.” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2021. <a href=\"https://doi.org/10.1112/blms.12442\">https://doi.org/10.1112/blms.12442</a>.","mla":"Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class for Toric Varieties.” <i>Bulletin of the London Mathematical Society</i>, vol. 53, no. 2, Wiley, 2021, pp. 560–74, doi:<a href=\"https://doi.org/10.1112/blms.12442\">10.1112/blms.12442</a>.","short":"K.P. Rychlewicz, Bulletin of the London Mathematical Society 53 (2021) 560–574.","ieee":"K. P. Rychlewicz, “The positivity of local equivariant Hirzebruch class for toric varieties,” <i>Bulletin of the London Mathematical Society</i>, vol. 53, no. 2. Wiley, pp. 560–574, 2021.","apa":"Rychlewicz, K. P. (2021). The positivity of local equivariant Hirzebruch class for toric varieties. <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/blms.12442\">https://doi.org/10.1112/blms.12442</a>"},"abstract":[{"lang":"eng","text":"The central object of investigation of this paper is the Hirzebruch class, a deformation of the Todd class, given by Hirzebruch (for smooth varieties). The generalization for singular varieties is due to Brasselet–Schürmann–Yokura. Following the work of Weber, we investigate its equivariant version for (possibly singular) toric varieties. The local decomposition of the Hirzebruch class to the fixed points of the torus action and a formula for the local class in terms of the defining fan are recalled. After this review part, we prove the positivity of local Hirzebruch classes for all toric varieties, thus proving false the alleged counterexample given by Weber."}],"article_processing_charge":"No","title":"The positivity of local equivariant Hirzebruch class for toric varieties","publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"year":"2021","publication_status":"published","publisher":"Wiley","department":[{"_id":"TaHa"}],"main_file_link":[{"url":"https://arxiv.org/abs/1910.10435","open_access":"1"}],"type":"journal_article","external_id":{"isi":["000594805800001"],"arxiv":["1910.10435"]},"day":"01","oa":1,"quality_controlled":"1","date_created":"2019-10-24T08:04:09Z","isi":1,"article_type":"original","language":[{"iso":"eng"}],"doi":"10.1112/blms.12442","_id":"6965","scopus_import":"1","oa_version":"Preprint"},{"author":[{"full_name":"He, Xiaoyu","first_name":"Xiaoyu","last_name":"He"},{"full_name":"Kwan, Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","last_name":"Kwan"}],"status":"public","issue":"3","publication":"Bulletin of the London Mathematical Society","volume":52,"month":"06","page":"515-529","date_published":"2020-06-01T00:00:00Z","citation":{"short":"X. He, M.A. Kwan, Bulletin of the London Mathematical Society 52 (2020) 515–529.","ieee":"X. He and M. A. Kwan, “Universality of random permutations,” <i>Bulletin of the London Mathematical Society</i>, vol. 52, no. 3. Wiley, pp. 515–529, 2020.","mla":"He, Xiaoyu, and Matthew Alan Kwan. “Universality of Random Permutations.” <i>Bulletin of the London Mathematical Society</i>, vol. 52, no. 3, Wiley, 2020, pp. 515–29, doi:<a href=\"https://doi.org/10.1112/blms.12345\">10.1112/blms.12345</a>.","apa":"He, X., &#38; Kwan, M. A. (2020). Universality of random permutations. <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/blms.12345\">https://doi.org/10.1112/blms.12345</a>","ama":"He X, Kwan MA. Universality of random permutations. <i>Bulletin of the London Mathematical Society</i>. 2020;52(3):515-529. doi:<a href=\"https://doi.org/10.1112/blms.12345\">10.1112/blms.12345</a>","chicago":"He, Xiaoyu, and Matthew Alan Kwan. “Universality of Random Permutations.” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2020. <a href=\"https://doi.org/10.1112/blms.12345\">https://doi.org/10.1112/blms.12345</a>.","ista":"He X, Kwan MA. 2020. Universality of random permutations. Bulletin of the London Mathematical Society. 52(3), 515–529."},"abstract":[{"lang":"eng","text":"It is a classical fact that for any ε>0, a random permutation of length n=(1+ε)k2/4 typically contains a monotone subsequence of length k. As a far-reaching generalization, Alon conjectured that a random permutation of this same length n is typically k-universal, meaning that it simultaneously contains every pattern of length k. He also made the simple observation that for n=O(k2logk), a random length-n permutation is typically k-universal. We make the first significant progress towards Alon's conjecture by showing that n=2000k2loglogk suffices."}],"intvolume":"        52","extern":"1","date_updated":"2023-02-23T14:01:23Z","publisher":"Wiley","year":"2020","publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1911.12878","open_access":"1"}],"type":"journal_article","oa":1,"external_id":{"arxiv":["1911.12878"]},"day":"01","title":"Universality of random permutations","article_processing_charge":"No","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"arxiv":1,"article_type":"original","language":[{"iso":"eng"}],"doi":"10.1112/blms.12345","scopus_import":"1","oa_version":"Preprint","_id":"9573","quality_controlled":"1","date_created":"2021-06-21T06:23:42Z"},{"intvolume":"        51","date_updated":"2025-07-10T11:53:52Z","date_published":"2019-10-01T00:00:00Z","abstract":[{"text":"The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asymptotic formula in mathematical physics. Here, we give a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic geometry.","lang":"eng"}],"citation":{"ista":"Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 51(5), 765–775.","ama":"Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli formula. <i>Bulletin of the London Mathematical Society</i>. 2019;51(5):765-775. doi:<a href=\"https://doi.org/10.1112/blms.12276\">10.1112/blms.12276</a>","chicago":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society, 2019. <a href=\"https://doi.org/10.1112/blms.12276\">https://doi.org/10.1112/blms.12276</a>.","mla":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” <i>Bulletin of the London Mathematical Society</i>, vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:<a href=\"https://doi.org/10.1112/blms.12276\">10.1112/blms.12276</a>.","ieee":"A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the Schläfli formula,” <i>Bulletin of the London Mathematical Society</i>, vol. 51, no. 5. London Mathematical Society, pp. 765–775, 2019.","short":"A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775.","apa":"Akopyan, A., &#38; Izmestiev, I. (2019). The Regge symmetry, confocal conics, and the Schläfli formula. <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/blms.12276\">https://doi.org/10.1112/blms.12276</a>"},"month":"10","ec_funded":1,"volume":51,"page":"765-775","status":"public","author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X"},{"full_name":"Izmestiev, Ivan","last_name":"Izmestiev","first_name":"Ivan"}],"publication":"Bulletin of the London Mathematical Society","issue":"5","quality_controlled":"1","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"isi":1,"date_created":"2019-08-11T21:59:23Z","language":[{"iso":"eng"}],"article_type":"original","_id":"6793","scopus_import":"1","oa_version":"Preprint","doi":"10.1112/blms.12276","article_processing_charge":"No","title":"The Regge symmetry, confocal conics, and the Schläfli formula","arxiv":1,"publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.04929"}],"department":[{"_id":"HeEd"}],"publication_status":"published","year":"2019","publisher":"London Mathematical Society","day":"01","external_id":{"isi":["000478560200001"],"arxiv":["1903.04929"]},"oa":1,"type":"journal_article"},{"publication_identifier":{"issn":["0024-6093"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","arxiv":1,"article_processing_charge":"No","title":"A tight estimate for the waist of the ball ","type":"journal_article","external_id":{"arxiv":["1608.06279"],"isi":["000407045900012"]},"day":"01","oa":1,"year":"2017","publication_status":"published","publisher":"Wiley","department":[{"_id":"HeEd"}],"main_file_link":[{"url":"https://arxiv.org/abs/1608.06279","open_access":"1"}],"date_created":"2018-12-11T11:48:02Z","isi":1,"project":[{"name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734"}],"quality_controlled":"1","doi":"10.1112/blms.12062","_id":"707","oa_version":"Preprint","scopus_import":"1","language":[{"iso":"eng"}],"page":"690 - 693","volume":49,"ec_funded":1,"month":"08","issue":"4","publication":"Bulletin of the London Mathematical Society","status":"public","author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"publist_id":"6982","date_updated":"2025-09-10T11:04:43Z","intvolume":"        49","corr_author":"1","abstract":[{"text":"We answer a question of M. Gromov on the waist of the unit ball.","lang":"eng"}],"citation":{"chicago":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2017. <a href=\"https://doi.org/10.1112/blms.12062\">https://doi.org/10.1112/blms.12062</a>.","ama":"Akopyan A, Karasev R. A tight estimate for the waist of the ball . <i>Bulletin of the London Mathematical Society</i>. 2017;49(4):690-693. doi:<a href=\"https://doi.org/10.1112/blms.12062\">10.1112/blms.12062</a>","apa":"Akopyan, A., &#38; Karasev, R. (2017). A tight estimate for the waist of the ball . <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/blms.12062\">https://doi.org/10.1112/blms.12062</a>","ieee":"A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,” <i>Bulletin of the London Mathematical Society</i>, vol. 49, no. 4. Wiley, pp. 690–693, 2017.","short":"A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017) 690–693.","mla":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” <i>Bulletin of the London Mathematical Society</i>, vol. 49, no. 4, Wiley, 2017, pp. 690–93, doi:<a href=\"https://doi.org/10.1112/blms.12062\">10.1112/blms.12062</a>.","ista":"Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 49(4), 690–693."},"date_published":"2017-08-01T00:00:00Z"}]