On the independence numbers of a matroid
type: Item
instance of: scholarly article
title: On the independence numbers of a matroid
zbMATH Open document ID: 0629.05020
DOI: 10.1016/0095-8956(89)90015-4
author: Yahya Ould Hamidoune
author: Isabelle Salaün
published in: Journal of Combinatorial Theory. Series B
publication date: 1989-01-01T00:00:00Z
review text: Given a finite subset E of a vector space of dimension 4. The number of k-independent subsets of E will be denoted by \(I_ k\). We prove that k \(I^ 2_ k\geq (k+1)I_{k-1}I_{k+1}+I_{k-1}I_ k\). The equality holds if and only if all 4-subsets of E are independent. We prove this relation for matroids of rank 4. In particular we prove Mason's conjecture on the independence numbers of a matroid for \(k=3\).
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 4023301
zbMATH Keywords: log-concave sequence
zbMATH Keywords: independence numbers of a matroid
MaRDI profile type: Publication
full work available at URL: 0095-8956(89)90015-4
OpenAlex ID: W2011321994
cites work: On the Independent Set Numbers of a Finite Matroid
cites work: On the unimodality of the independent set numbers of a class of matroids
cites work: On the points-lines-planes conjecture
cites work: Two combinatorial applications of the Aleksandrov-Fenchel inequalities
cites work: Q4111952
description: scientific article; zbMATH DE number 4023301