On a unimodality conjecture in matroid theory

Dukes, W.M.B. (2002) On a unimodality conjecture in matroid theory. Discrete Mathematics and Theoretical Computer Science, 5 (1). pp. 181-190. ISSN 1365-8050

Abstract

A certain unimodal conjecture in matroid theory states 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-2 matroids into the class of loopless rank-3 matroids. Similar inequalities are proven for the number of non-isomorphic loopless matroids, loopless matroids and matroids.

ORCID iDs

Dukes, W.M.B. ORCID: https://orcid.org/0000-0002-2779-2680

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• Item metadata

  Item type:	Article
  ID code:	50746
  Dates:	Date Event 2002 Published
  Subjects:	Science > Mathematics > Electronic computers. Computer science
  Department:	Faculty of Science > Computer and Information Sciences
  Depositing user:	Pure Administrator
  Date deposited:	10 Dec 2014 11:52
  Last modified:	11 Nov 2024 10:53
  Related URLs:	Journal or Publication
  URI:	https://strathprints.strath.ac.uk/id/eprint/50746