On a Unimodal Conjecture in Matroid Theory

Dukes, W.M.B. (2001) On a Unimodal Conjecture in Matroid Theory. (Preprint)

Share Twitter Facebook Email

[img] Text
DIAS-STP-01-13.pdf

Download (183kB)

Abstract

A certain unimodal conjecture in matroid theory states that the number of rank-r matroids on a set of size n is unimodal in r and attains its maximum at r = ⌊n/2⌋. We show that this conjecture holds up to r = 3 by constructing a map from a class of rank-3 matroids. Similar inequalities are proven for the number of non-isomorphic loopless matroids, loopless matroids and matroids.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 13 Jun 2018 13:09
Last Modified: 17 Jul 2018 11:52
URI: http://dair.dias.ie/id/eprint/442

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year