On the number of matroids on a finite set

W.M.B. Dukes

Research output: Contribution to journalArticlepeer-review


In this paper we highlight some enumerative results concerning matroids of low rank and prove the tail-ends of various sequences involving the number of matroids on a finite set to be log-convex. We give a recursion for a new, slightly improved, lower bound on the number of rank-r matroids on n elements when n=2m-1. We also prove an adjacent result showing the point-lines-planes conjecture to be true if and only if it is true for a special sub-collection of matroids. Two new tables are also presented, giving the number of paving matroids on at most eight elements.
Original languageEnglish
Article numberB51g
Number of pages12
JournalSéminaire Lotharingien de Combinatoire
Publication statusPublished - 2004


  • matroid theory
  • finite set
  • paving matroids


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