---
res:
bibo_abstract:
- '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.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Matthew Alan
foaf_name: Kwan, Matthew Alan
foaf_surname: Kwan
foaf_workInfoHomepage: http://www.librecat.org/personId=5fca0887-a1db-11eb-95d1-ca9d5e0453b3
orcid: 0000-0002-4003-7567
- foaf_Person:
foaf_givenName: Ashwin
foaf_name: Sah, Ashwin
foaf_surname: Sah
- foaf_Person:
foaf_givenName: Mehtaab
foaf_name: Sawhney, Mehtaab
foaf_surname: Sawhney
bibo_doi: 10.5802/crmath.423
bibo_issue: G2
bibo_volume: 361
dct_date: 2023^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/1631-073X
- http://id.crossref.org/issn/1778-3569
dct_language: eng
dct_publisher: Academie des Sciences@
dct_title: Enumerating matroids and linear spaces@
...