On a unimodality conjecture in matroid theory

W.M.B. Dukes

Research output: Contribution to journalArticle

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.
LanguageEnglish
Pages181-190
Number of pages10
JournalDiscrete Mathematics and Theoretical Computer Science
Volume5
Issue number1
Publication statusPublished - 2002

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Unimodality
Matroid

Keywords

  • matroid theory
  • unimodal conjecture
  • rank 2 matroids
  • rank 3 matroids

Cite this

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On a unimodality conjecture in matroid theory. / Dukes, W.M.B.

In: Discrete Mathematics and Theoretical Computer Science, Vol. 5, No. 1, 2002, p. 181-190.

Research output: Contribution to journalArticle

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