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Medientyp:
E-Artikel
Titel:
Enumerating matroids and linear spaces
Beteiligte:
Kwan, Matthew Alan
[Verfasser:in];
Sah, Ashwin
[Verfasser:in];
Sawhney, Mehtaab
[Verfasser:in]
Erschienen:
Academie des Sciences, 2023
Erschienen in:Kwan MA, Sah A, Sawhney M. Enumerating matroids and linear spaces. Comptes Rendus Mathematique . 2023;361(G2):565-575. doi: 10.5802/crmath.423
Sprache:
Englisch
DOI:
https://doi.org/10.5802/crmath.423
ISSN:
1631-073X;
1778-3569
Entstehung:
Anmerkungen:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Beschreibung:
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.