[{"date_published":"2023-02-01T00:00:00Z","month":"02","license":"https://creativecommons.org/licenses/by/4.0/","file":[{"file_size":598097,"file_id":"15174","relation":"main_file","content_type":"application/pdf","checksum":"d1d0e0a854a79ae95fb66d75d9117a68","success":1,"file_name":"2023_ComptesRendusMath_Kwan.pdf","date_created":"2024-03-25T07:21:52Z","creator":"dernst","access_level":"open_access","date_updated":"2024-03-25T07:21:52Z"}],"date_updated":"2025-09-09T14:26:32Z","department":[{"_id":"MaKw"}],"acknowledgement":"Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE-1745302. Sah was supported by the PD Soros Fellowship.\r\nWe thank Michael Simkin for helpful comments on the manuscript. We thank Zach Hunter for\r\nseveral corrections.","date_created":"2024-03-24T23:01:00Z","quality_controlled":"1","status":"public","ddc":["510"],"scopus_import":"1","intvolume":"       361","publication":"Comptes Rendus Mathematique","volume":361,"year":"2023","publisher":"Academie des Sciences","author":[{"full_name":"Kwan, Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","last_name":"Kwan"},{"last_name":"Sah","full_name":"Sah, Ashwin","first_name":"Ashwin"},{"full_name":"Sawhney, Mehtaab","first_name":"Mehtaab","last_name":"Sawhney"}],"file_date_updated":"2024-03-25T07:21:52Z","oa":1,"tmp":{"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","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"We show that the number of linear spaces on a set of n points and the number of rank-3 matroids on a ground set of size n are both of the form (cn+o(n))n2/6, where c=e3√/2−3(1+3–√)/2. This is the final piece of the puzzle for enumerating fixed-rank matroids at this level of accuracy: the numbers of rank-1 and rank-2 matroids on a ground set of size n have exact representations in terms of well-known combinatorial functions, and it was recently proved by van der Hofstad, Pendavingh, and van der Pol that for constant r≥4 there are (e1−rn+o(n))nr−1/r! rank-r matroids on a ground set of size n. In our proof, we introduce a new approach for bounding the number of clique decompositions of a complete graph, using quasirandomness instead of the so-called entropy method that is common in this area."}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Enumerating matroids and linear spaces","publication_identifier":{"issn":["1631-073X"],"eissn":["1778-3569"]},"publication_status":"published","external_id":{"isi":["001167671400009"],"arxiv":["2112.03788"]},"citation":{"mla":"Kwan, Matthew Alan, et al. “Enumerating Matroids and Linear Spaces.” <i>Comptes Rendus Mathematique</i>, vol. 361, no. G2, Academie des Sciences, 2023, pp. 565–75, doi:<a href=\"https://doi.org/10.5802/crmath.423\">10.5802/crmath.423</a>.","ieee":"M. A. Kwan, A. Sah, and M. Sawhney, “Enumerating matroids and linear spaces,” <i>Comptes Rendus Mathematique</i>, vol. 361, no. G2. Academie des Sciences, pp. 565–575, 2023.","short":"M.A. Kwan, A. Sah, M. Sawhney, Comptes Rendus Mathematique 361 (2023) 565–575.","ama":"Kwan MA, Sah A, Sawhney M. Enumerating matroids and linear spaces. <i>Comptes Rendus Mathematique</i>. 2023;361(G2):565-575. doi:<a href=\"https://doi.org/10.5802/crmath.423\">10.5802/crmath.423</a>","apa":"Kwan, M. A., Sah, A., &#38; Sawhney, M. (2023). Enumerating matroids and linear spaces. <i>Comptes Rendus Mathematique</i>. Academie des Sciences. <a href=\"https://doi.org/10.5802/crmath.423\">https://doi.org/10.5802/crmath.423</a>","ista":"Kwan MA, Sah A, Sawhney M. 2023. Enumerating matroids and linear spaces. Comptes Rendus Mathematique. 361(G2), 565–575.","chicago":"Kwan, Matthew Alan, Ashwin Sah, and Mehtaab Sawhney. “Enumerating Matroids and Linear Spaces.” <i>Comptes Rendus Mathematique</i>. Academie des Sciences, 2023. <a href=\"https://doi.org/10.5802/crmath.423\">https://doi.org/10.5802/crmath.423</a>."},"article_processing_charge":"Yes","fulldoi":"https://doi.org/10.5802/crmath.423","oa_version":"Published Version","language":[{"iso":"eng"}],"day":"01","_id":"15173","doi":"10.5802/crmath.423","page":"565-575","article_type":"original","issue":"G2","isi":1,"arxiv":1,"has_accepted_license":"1","type":"journal_article"},{"citation":{"ista":"Fox J, Wigderson Y, Zhao Y. 2020. A short proof of the canonical polynomial van der Waerden theorem. Comptes Rendus Mathématique. 358(8), 957–959.","chicago":"Fox, Jacob, Yuval Wigderson, and Yufei Zhao. “A Short Proof of the Canonical Polynomial van Der Waerden Theorem.” <i>Comptes Rendus Mathématique</i>. Académie des Sciences, 2020. <a href=\"https://doi.org/10.5802/crmath.101\">https://doi.org/10.5802/crmath.101</a>.","mla":"Fox, Jacob, et al. “A Short Proof of the Canonical Polynomial van Der Waerden Theorem.” <i>Comptes Rendus Mathématique</i>, vol. 358, no. 8, Académie des Sciences, 2020, pp. 957–59, doi:<a href=\"https://doi.org/10.5802/crmath.101\">10.5802/crmath.101</a>.","ieee":"J. Fox, Y. Wigderson, and Y. Zhao, “A short proof of the canonical polynomial van der Waerden theorem,” <i>Comptes Rendus Mathématique</i>, vol. 358, no. 8. Académie des Sciences, pp. 957–959, 2020.","short":"J. Fox, Y. Wigderson, Y. Zhao, Comptes Rendus Mathématique 358 (2020) 957–959.","ama":"Fox J, Wigderson Y, Zhao Y. A short proof of the canonical polynomial van der Waerden theorem. <i>Comptes Rendus Mathématique</i>. 2020;358(8):957-959. doi:<a href=\"https://doi.org/10.5802/crmath.101\">10.5802/crmath.101</a>","apa":"Fox, J., Wigderson, Y., &#38; Zhao, Y. (2020). A short proof of the canonical polynomial van der Waerden theorem. <i>Comptes Rendus Mathématique</i>. Académie des Sciences. <a href=\"https://doi.org/10.5802/crmath.101\">https://doi.org/10.5802/crmath.101</a>"},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2005.04135"}],"extern":"1","publication_identifier":{"issn":["1631-073X"],"eissn":["1778-3569"]},"publication_status":"published","external_id":{"arxiv":["2005.04135"]},"title":"A short proof of the canonical polynomial van der Waerden theorem","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","mathsc":["05D10","11B30"],"type":"journal_article","issue":"8","arxiv":1,"page":"957-959","article_type":"original","doi":"10.5802/crmath.101","oa_version":"Preprint","fulldoi":"https://doi.org/10.5802/crmath.101","language":[{"iso":"eng"}],"day":"03","_id":"22182","article_processing_charge":"No","date_created":"2026-06-29T11:00:09Z","date_updated":"2026-07-14T09:19:20Z","OA_place":"repository","month":"12","date_published":"2020-12-03T00:00:00Z","abstract":[{"lang":"eng","text":"We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girão."}],"author":[{"last_name":"Fox","first_name":"Jacob","full_name":"Fox, Jacob"},{"last_name":"Wigderson","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","first_name":"Yuval","full_name":"Wigderson, Yuval"},{"first_name":"Yufei","full_name":"Zhao, Yufei","last_name":"Zhao"}],"oa":1,"publisher":"Académie des Sciences","publication":"Comptes Rendus Mathématique","volume":358,"year":"2020","intvolume":"       358","OA_type":"green","status":"public","quality_controlled":"1","scopus_import":"1"}]