{"intvolume":"       361","publication_status":"published","author":[{"last_name":"Kwan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan"},{"last_name":"Sah","first_name":"Ashwin","full_name":"Sah, Ashwin"},{"first_name":"Mehtaab","last_name":"Sawhney","full_name":"Sawhney, Mehtaab"}],"article_type":"original","type":"journal_article","title":"Enumerating matroids and linear spaces","language":[{"iso":"eng"}],"_id":"15173","publication":"Comptes Rendus Mathematique","ddc":["510"],"date_published":"2023-02-01T00:00:00Z","status":"public","abstract":[{"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.","lang":"eng"}],"month":"02","page":"565-575","quality_controlled":"1","article_processing_charge":"Yes","publisher":"Academie des Sciences","publication_identifier":{"issn":["1631-073X"],"eissn":["1778-3569"]},"external_id":{"arxiv":["2112.03788"]},"has_accepted_license":"1","oa":1,"date_created":"2024-03-24T23:01:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"scopus_import":"1","issue":"G2","year":"2023","volume":361,"file_date_updated":"2024-03-25T07:21:52Z","citation":{"short":"M.A. Kwan, A. Sah, M. Sawhney, Comptes Rendus Mathematique 361 (2023) 565–575.","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.","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>","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>","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>.","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>."},"date_updated":"2024-03-25T07:23:15Z","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.","doi":"10.5802/crmath.423","file":[{"file_id":"15174","success":1,"creator":"dernst","relation":"main_file","date_created":"2024-03-25T07:21:52Z","access_level":"open_access","date_updated":"2024-03-25T07:21:52Z","checksum":"d1d0e0a854a79ae95fb66d75d9117a68","file_name":"2023_ComptesRendusMath_Kwan.pdf","file_size":598097,"content_type":"application/pdf"}],"oa_version":"Published Version"}