Size functions of subgeometry-closed classes of representable combinatorial geometries
type: Item
instance of: scholarly article
title: Size functions of subgeometry-closed classes of representable combinatorial geometries
zbMATH Open document ID: 0968.52009
DOI: 10.1016/S0012-365X(00)00108-4
author: Joseph E. Bonin
author: Hongxun Qin
published in: Discrete Mathematics
publication date: 2001-09-11T00:00:00Z
review text: Let \(F_q\) be a finite field of characteristic \(q.\) A projective geometry \(PG(r, F_q)\) is the rank \(r\) matroid on the points of the \((r-1)\)-dimensional projective vector space over \(F_q.\) If we delete from \(PG(r, F_q)\) all the points of a hyperplane we obtain the affine geometry \(AG(r, F_q).\) Let \(ex_q(M; r)\) be the number of \(F_q\)-representable simple matroids of rank \(r\) that have no submatroid (restriction) isomorphic to a fixed simple matroid \(M.\) The purpose of this paper is to find \(ex_q(M; r)\) for several infinite families of \(M.\) In particular it is proved that \[ \lim_{r\to \infty} \frac {ex_2(AG(r, F_2); r)} {2^r-1}=0. \]
reviewed by: Raul Cordovil
Mathematics Subject Classification ID: 52B40
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 1533338
zbMATH Keywords: matroid
zbMATH Keywords: extremal matroid theory
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1533338