{"intvolume":"        56","language":[{"iso":"eng"}],"quality_controlled":"1","oa":1,"corr_author":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"796-802","file_date_updated":"2024-07-16T10:35:10Z","file":[{"file_name":"2024_BulletinLondonMathSoc_Ivanov.pdf","access_level":"open_access","relation":"main_file","file_id":"17259","checksum":"30ea0694757bc668cf7cd15ae357b35e","success":1,"date_created":"2024-07-16T10:35:10Z","content_type":"application/pdf","creator":"dernst","file_size":111756,"date_updated":"2024-07-16T10:35:10Z"}],"date_published":"2024-02-01T00:00:00Z","publication_status":"published","day":"01","publication":"Bulletin of the London Mathematical Society","author":[{"first_name":"Grigory","full_name":"Ivanov, Grigory","last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E"},{"first_name":"Márton","full_name":"Naszódi, Márton","last_name":"Naszódi"}],"doi":"10.1112/blms.12965","_id":"14660","volume":56,"external_id":{"arxiv":["2212.04308"]},"issue":"2","publisher":"London Mathematical Society","abstract":[{"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.","lang":"eng"}],"ddc":["510"],"year":"2024","publication_identifier":{"eissn":["1469-2120"],"issn":["0024-6093"]},"oa_version":"Published Version","department":[{"_id":"UlWa"}],"article_type":"original","status":"public","date_created":"2023-12-10T23:00:58Z","has_accepted_license":"1","citation":{"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>","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>.","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>.","short":"G. Ivanov, M. Naszódi, Bulletin of the London Mathematical Society 56 (2024) 796–802.","ista":"Ivanov G, Naszódi M. 2024. Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society. 56(2), 796–802.","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>","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."},"type":"journal_article","month":"02","date_updated":"2024-07-16T10:35:44Z","title":"Quantitative Steinitz theorem: A polynomial bound","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","article_processing_charge":"Yes (via OA deal)","scopus_import":"1"}