[{"oa":1,"ec_funded":1,"type":"journal_article","isi":1,"date_published":"2025-03-14T00:00:00Z","article_number":"e55","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","file":[{"file_id":"19468","success":1,"date_updated":"2025-04-03T11:24:35Z","creator":"dernst","file_name":"2025_ForumMathSigma_Anastos.pdf","checksum":"f396270ad78c1ed67095c8e5a66fca26","relation":"main_file","date_created":"2025-04-03T11:24:35Z","content_type":"application/pdf","access_level":"open_access","file_size":630297}],"year":"2025","article_processing_charge":"Yes","publication_status":"published","intvolume":"        13","language":[{"iso":"eng"}],"OA_type":"gold","publisher":"Cambridge University Press","date_created":"2025-03-20T12:59:14Z","has_accepted_license":"1","abstract":[{"lang":"eng","text":"An ordered r-matching is an r-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of r-dimensional orders. The theory of ordered 2-matchings is well developed and has connections and applications to extremal and enumerative combinatorics, probability and geometry. On the other hand, in the case  r≥3 much less is known, largely due to a lack of powerful bijective tools. Recently, Dudek, Grytczuk and Ruciński made some first steps towards a general theory of ordered r-matchings, and in this paper we substantially improve several of their results and introduce some new directions of study. Many intriguing open questions remain."}],"corr_author":"1","month":"03","status":"public","ddc":["510"],"publication":"Forum of Mathematics, Sigma","external_id":{"arxiv":["2308.12268"],"isi":["001444429200001"]},"license":"https://creativecommons.org/licenses/by/4.0/","OA_place":"publisher","arxiv":1,"acknowledgement":"We would like to thank Timo Seppäläinen for some illuminating discussion about random high-dimensional orders and for bringing our attention to [59]. We would also like to thank the referees for helpful feedback. Michael Anastos is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101034413. Matthew Kwan is supported by ERC Starting Grant ‘RANDSTRUCT’ No. 101076777, also funded by the European Union. Zhihan Jin and Benny Sudakov are supported by SNSF grant 200021-228014.","article_type":"original","publication_identifier":{"issn":["2050-5094"]},"file_date_updated":"2025-04-03T11:24:35Z","day":"14","date_updated":"2025-09-30T11:18:57Z","title":"Extremal, enumerative and probabilistic results on ordered hypergraph matchings","author":[{"full_name":"Anastos, Michael","id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb","first_name":"Michael","last_name":"Anastos"},{"first_name":"Zhihan","last_name":"Jin","full_name":"Jin, Zhihan"},{"first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","last_name":"Kwan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan"},{"first_name":"Benny","last_name":"Sudakov","full_name":"Sudakov, Benny"}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"apa":"Anastos, M., Jin, Z., Kwan, M. A., &#38; Sudakov, B. (2025). Extremal, enumerative and probabilistic results on ordered hypergraph matchings. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2024.144\">https://doi.org/10.1017/fms.2024.144</a>","ama":"Anastos M, Jin Z, Kwan MA, Sudakov B. Extremal, enumerative and probabilistic results on ordered hypergraph matchings. <i>Forum of Mathematics, Sigma</i>. 2025;13. doi:<a href=\"https://doi.org/10.1017/fms.2024.144\">10.1017/fms.2024.144</a>","ista":"Anastos M, Jin Z, Kwan MA, Sudakov B. 2025. Extremal, enumerative and probabilistic results on ordered hypergraph matchings. Forum of Mathematics, Sigma. 13, e55.","mla":"Anastos, Michael, et al. “Extremal, Enumerative and Probabilistic Results on Ordered Hypergraph Matchings.” <i>Forum of Mathematics, Sigma</i>, vol. 13, e55, Cambridge University Press, 2025, doi:<a href=\"https://doi.org/10.1017/fms.2024.144\">10.1017/fms.2024.144</a>.","ieee":"M. Anastos, Z. Jin, M. A. Kwan, and B. Sudakov, “Extremal, enumerative and probabilistic results on ordered hypergraph matchings,” <i>Forum of Mathematics, Sigma</i>, vol. 13. Cambridge University Press, 2025.","short":"M. Anastos, Z. Jin, M.A. Kwan, B. Sudakov, Forum of Mathematics, Sigma 13 (2025).","chicago":"Anastos, Michael, Zhihan Jin, Matthew Alan Kwan, and Benny Sudakov. “Extremal, Enumerative and Probabilistic Results on Ordered Hypergraph Matchings.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/fms.2024.144\">https://doi.org/10.1017/fms.2024.144</a>."},"doi":"10.1017/fms.2024.144","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program"},{"name":"Randomness and structure in combinatorics","grant_number":"101076777","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"}],"volume":13,"scopus_import":"1","department":[{"_id":"MaKw"}],"oa_version":"Published Version","quality_controlled":"1","_id":"19433"},{"date_created":"2026-06-29T10:51:07Z","abstract":[{"text":"The triangle removal states that if G contains  edge-disjoint triangles, then G contains  triangles. Unfortunately, there are no sensible bounds on the order of growth of , and at any rate, it is known that  is not polynomial in . Csaba recently obtained an asymmetric variant of the triangle removal, stating that if G contains  edge-disjoint triangles, then G contains  copies of . To this end, he devised a new variant of Szemerédi’s regularity lemma. We obtain the following results:\r\n\r\n• We first give a regularity-free proof of Csaba’s theorem, which improves the number of copies of  to the optimal number .\r\n\r\n• We say that H is -abundant if every graph containing  edge-disjoint triangles has  copies of H. It is easy to see that a -abundant graph must be triangle-free and tripartite. Given our first result, it is natural to ask if all triangle-free tripartite graphs are -abundant. Our second result is that assuming a well-known conjecture of Ruzsa in additive number theory, the answer to this question is negative.\r\n\r\nOur proofs use a mix of combinatorial, number-theoretic, probabilistic and Ramsey-type arguments.","lang":"eng"}],"publisher":"Cambridge University Press","OA_type":"green","language":[{"iso":"eng"}],"intvolume":"        13","mathsc":["05C35","11B75"],"month":"02","publication":"Forum of Mathematics, Sigma","status":"public","type":"journal_article","oa":1,"publication_status":"published","article_processing_charge":"No","year":"2025","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"e38","date_published":"2025-02-10T00:00:00Z","scopus_import":"1","volume":13,"doi":"10.1017/fms.2024.68","citation":{"short":"L. Gishboliner, A. Shapira, Y. Wigderson, Forum of Mathematics, Sigma 13 (2025).","chicago":"Gishboliner, Lior, Asaf Shapira, and Yuval Wigderson. “An Efficient Asymmetric Removal Lemma and Its Limitations.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/fms.2024.68\">https://doi.org/10.1017/fms.2024.68</a>.","apa":"Gishboliner, L., Shapira, A., &#38; Wigderson, Y. (2025). An efficient asymmetric removal lemma and its limitations. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2024.68\">https://doi.org/10.1017/fms.2024.68</a>","ista":"Gishboliner L, Shapira A, Wigderson Y. 2025. An efficient asymmetric removal lemma and its limitations. Forum of Mathematics, Sigma. 13, e38.","ama":"Gishboliner L, Shapira A, Wigderson Y. An efficient asymmetric removal lemma and its limitations. <i>Forum of Mathematics, Sigma</i>. 2025;13. doi:<a href=\"https://doi.org/10.1017/fms.2024.68\">10.1017/fms.2024.68</a>","mla":"Gishboliner, Lior, et al. “An Efficient Asymmetric Removal Lemma and Its Limitations.” <i>Forum of Mathematics, Sigma</i>, vol. 13, e38, Cambridge University Press, 2025, doi:<a href=\"https://doi.org/10.1017/fms.2024.68\">10.1017/fms.2024.68</a>.","ieee":"L. Gishboliner, A. Shapira, and Y. Wigderson, “An efficient asymmetric removal lemma and its limitations,” <i>Forum of Mathematics, Sigma</i>, vol. 13. Cambridge University Press, 2025."},"_id":"22158","extern":"1","oa_version":"Preprint","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2301.07693"}],"day":"10","article_type":"original","publication_identifier":{"issn":["2050-5094"]},"arxiv":1,"OA_place":"repository","external_id":{"arxiv":["2301.07693"]},"author":[{"full_name":"Gishboliner, Lior","first_name":"Lior","last_name":"Gishboliner"},{"last_name":"Shapira","first_name":"Asaf","full_name":"Shapira, Asaf"},{"id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","full_name":"Wigderson, Yuval","last_name":"Wigderson","first_name":"Yuval"}],"title":"An efficient asymmetric removal lemma and its limitations","date_updated":"2026-07-08T10:31:22Z"},{"author":[{"orcid":"0000-0003-4476-2288","last_name":"Lauritsen","first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2026-04-07T13:01:40Z","title":"Pressure of a dilute spin-polarized Fermi gas: Lower bound","arxiv":1,"publication_identifier":{"issn":["2050-5094"]},"file_date_updated":"2024-09-23T09:56:17Z","article_type":"original","related_material":{"record":[{"status":"public","id":"18135","relation":"dissertation_contains"}]},"acknowledgement":"Financial support by the Austrian Science Fund (FWF) through grant DOI: 10.55776/I6427 (as part of the SFB/TRR 352) is gratefully acknowledged.","day":"09","external_id":{"arxiv":["2407.05990"],"isi":["001307817400001"]},"quality_controlled":"1","oa_version":"Published Version","_id":"18107","volume":12,"scopus_import":"1","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"ama":"Lauritsen AB, Seiringer R. Pressure of a dilute spin-polarized Fermi gas: Lower bound. <i>Forum of Mathematics, Sigma</i>. 2024;12. doi:<a href=\"https://doi.org/10.1017/fms.2024.56\">10.1017/fms.2024.56</a>","ista":"Lauritsen AB, Seiringer R. 2024. Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. 12, e78.","apa":"Lauritsen, A. B., &#38; Seiringer, R. (2024). Pressure of a dilute spin-polarized Fermi gas: Lower bound. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2024.56\">https://doi.org/10.1017/fms.2024.56</a>","mla":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” <i>Forum of Mathematics, Sigma</i>, vol. 12, e78, Cambridge University Press, 2024, doi:<a href=\"https://doi.org/10.1017/fms.2024.56\">10.1017/fms.2024.56</a>.","ieee":"A. B. Lauritsen and R. Seiringer, “Pressure of a dilute spin-polarized Fermi gas: Lower bound,” <i>Forum of Mathematics, Sigma</i>, vol. 12. Cambridge University Press, 2024.","short":"A.B. Lauritsen, R. Seiringer, Forum of Mathematics, Sigma 12 (2024).","chicago":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2024. <a href=\"https://doi.org/10.1017/fms.2024.56\">https://doi.org/10.1017/fms.2024.56</a>."},"doi":"10.1017/fms.2024.56","project":[{"_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427"}],"file":[{"success":1,"file_id":"18126","date_updated":"2024-09-23T09:56:17Z","file_name":"2024_ForumMath_Lauritsen.pdf","creator":"dernst","checksum":"330b881240013213a8e08538fec13d29","date_created":"2024-09-23T09:56:17Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_size":599886}],"year":"2024","article_processing_charge":"Yes","publication_status":"published","article_number":"e78","date_published":"2024-09-09T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"isi":1,"type":"journal_article","publication":"Forum of Mathematics, Sigma","ddc":["510"],"status":"public","corr_author":"1","month":"09","publisher":"Cambridge University Press","abstract":[{"lang":"eng","text":"We consider a dilute fully spin-polarized Fermi gas at positive temperature in dimensions  d∈{1,2,3} . We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order  adρ2+2/d, where a is the p-wave scattering length of the repulsive interaction and  ρ  is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237–260)."}],"date_created":"2024-09-20T12:25:25Z","has_accepted_license":"1","intvolume":"        12","language":[{"iso":"eng"}]},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_number":"e96","date_published":"2022-10-27T00:00:00Z","publication_status":"published","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"year":"2022","article_processing_charge":"No","file":[{"file_id":"12356","success":1,"date_updated":"2023-01-24T10:02:40Z","relation":"main_file","date_created":"2023-01-24T10:02:40Z","creator":"dernst","checksum":"94a049aeb1eea5497aa097712a73c400","file_name":"2022_ForumMath_Cipolloni.pdf","file_size":817089,"content_type":"application/pdf","access_level":"open_access"}],"type":"journal_article","ec_funded":1,"isi":1,"oa":1,"status":"public","ddc":["510"],"month":"10","corr_author":"1","publication":"Forum of Mathematics, Sigma","language":[{"iso":"eng"}],"intvolume":"        10","has_accepted_license":"1","abstract":[{"lang":"eng","text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables."}],"date_created":"2023-01-12T12:07:30Z","publisher":"Cambridge University Press","title":"Rank-uniform local law for Wigner matrices","date_updated":"2025-04-14T07:57:18Z","author":[{"first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"external_id":{"isi":["000873719200001"]},"day":"27","acknowledgement":"L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","publication_identifier":{"issn":["2050-5094"]},"article_type":"original","file_date_updated":"2023-01-24T10:02:40Z","_id":"12148","quality_controlled":"1","oa_version":"Published Version","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"citation":{"mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e96, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022)."},"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"doi":"10.1017/fms.2022.86","department":[{"_id":"LaEr"}],"scopus_import":"1","volume":10},{"publication_status":"published","article_processing_charge":"Yes","year":"2022","article_number":"e46","date_published":"2022-05-17T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"type":"journal_article","status":"public","ddc":["510"],"month":"05","publication":"Forum of Mathematics, Sigma","publisher":"Cambridge University Press","date_created":"2025-04-05T10:51:00Z","has_accepted_license":"1","abstract":[{"text":"Using a recent breakthrough of Smith [18], we improve the results of Fouvry and Klüners [4, 5] on the solubility of the negative Pell equation. Let D denote the set of positive squarefree integers having no prime factors congruent to 3 modulo 4 . Stevenhagen [19] conjectured that the density of d in D such that the negative Pell equation x2−dy2=−1 is solvable with x,y∈Z is 58.1% , to the nearest tenth of a percent. By studying the distribution of the 8 -rank of narrow class groups Cl+(d) of Q(√d) , we prove that the infimum of this density is at least 53.8% .","lang":"eng"}],"intvolume":"        10","language":[{"iso":"eng"}],"OA_type":"gold","author":[{"last_name":"Chan","orcid":"0000-0001-8467-4106","first_name":"Yik Tung","full_name":"Chan, Yik Tung","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1"},{"last_name":"Koymans","first_name":"Peter","full_name":"Koymans, Peter"},{"first_name":"Djordjo","last_name":"Milovic","full_name":"Milovic, Djordjo"},{"last_name":"Pagano","first_name":"Carlo","full_name":"Pagano, Carlo"}],"title":"The 8-rank of the narrow class group and the negative Pell equation","date_updated":"2025-07-10T11:51:47Z","arxiv":1,"DOAJ_listed":"1","day":"17","publication_identifier":{"issn":["2050-5094"]},"article_type":"original","external_id":{"arxiv":["1908.01752"]},"OA_place":"publisher","oa_version":"Published Version","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.1017/fms.2022.40","open_access":"1"}],"extern":"1","_id":"19491","volume":10,"scopus_import":"1","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"ieee":"S. Chan, P. Koymans, D. Milovic, and C. Pagano, “The 8-rank of the narrow class group and the negative Pell equation,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","mla":"Chan, Stephanie, et al. “The 8-Rank of the Narrow Class Group and the Negative Pell Equation.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e46, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2022.40\">10.1017/fms.2022.40</a>.","apa":"Chan, S., Koymans, P., Milovic, D., &#38; Pagano, C. (2022). The 8-rank of the narrow class group and the negative Pell equation. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2022.40\">https://doi.org/10.1017/fms.2022.40</a>","ama":"Chan S, Koymans P, Milovic D, Pagano C. The 8-rank of the narrow class group and the negative Pell equation. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2022.40\">10.1017/fms.2022.40</a>","ista":"Chan S, Koymans P, Milovic D, Pagano C. 2022. The 8-rank of the narrow class group and the negative Pell equation. Forum of Mathematics, Sigma. 10, e46.","chicago":"Chan, Stephanie, Peter Koymans, Djordjo Milovic, and Carlo Pagano. “The 8-Rank of the Narrow Class Group and the Negative Pell Equation.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2022.40\">https://doi.org/10.1017/fms.2022.40</a>.","short":"S. Chan, P. Koymans, D. Milovic, C. Pagano, Forum of Mathematics, Sigma 10 (2022)."},"doi":"10.1017/fms.2022.40"},{"abstract":[{"text":"We  prove  that  any  cyclic  quadrilateral  can  be  inscribed  in  any  closed  convex C1-curve.  The smoothness condition is not required if the quadrilateral is a rectangle.","lang":"eng"}],"has_accepted_license":"1","date_created":"2019-04-30T06:09:57Z","publisher":"Cambridge University Press","language":[{"iso":"eng"}],"intvolume":"         6","ddc":["510"],"month":"05","corr_author":"1","status":"public","publication":"Forum of Mathematics, Sigma","ec_funded":1,"isi":1,"type":"journal_article","oa":1,"article_processing_charge":"No","year":"2018","publication_status":"published","file":[{"file_id":"6356","date_updated":"2020-07-14T12:47:28Z","checksum":"5a71b24ba712a3eb2e46165a38fbc30a","file_name":"2018_ForumMahtematics_Akopyan.pdf","creator":"dernst","relation":"main_file","date_created":"2019-04-30T06:14:58Z","content_type":"application/pdf","access_level":"open_access","file_size":249246}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_number":"e7","date_published":"2018-05-31T00:00:00Z","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"volume":6,"project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"doi":"10.1017/fms.2018.7","citation":{"mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” <i>Forum of Mathematics, Sigma</i>, vol. 6, e7, Cambridge University Press, 2018, doi:<a href=\"https://doi.org/10.1017/fms.2018.7\">10.1017/fms.2018.7</a>.","ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” <i>Forum of Mathematics, Sigma</i>, vol. 6. Cambridge University Press, 2018.","ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. <i>Forum of Mathematics, Sigma</i>. 2018;6. doi:<a href=\"https://doi.org/10.1017/fms.2018.7\">10.1017/fms.2018.7</a>","apa":"Akopyan, A., &#38; Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2018.7\">https://doi.org/10.1017/fms.2018.7</a>","chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2018. <a href=\"https://doi.org/10.1017/fms.2018.7\">https://doi.org/10.1017/fms.2018.7</a>.","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018)."},"_id":"6355","quality_controlled":"1","oa_version":"Published Version","publication_identifier":{"issn":["2050-5094"]},"related_material":{"record":[{"id":"8156","relation":"dissertation_contains","status":"public"}]},"file_date_updated":"2020-07-14T12:47:28Z","day":"31","arxiv":1,"external_id":{"arxiv":["1712.10205"],"isi":["000433915500001"]},"author":[{"orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"},{"last_name":"Avvakumov","orcid":"0000-0002-7840-5062","first_name":"Sergey","full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2026-04-08T07:25:54Z","title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve"}]