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