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