On a unimodality conjecture in matroid theory

W.M.B. Dukes

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)181-190
Number of pages10
JournalDiscrete Mathematics and Theoretical Computer Science
Issue number1
Publication statusPublished - 2002


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


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