On the number of matroids on a finite set
Dukes, W.M.B. (2004) On the number of matroids on a finite set. Séminaire Lotharingien de Combinatoire, 51. B51g. ISSN 1286-4889
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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.
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Item type: Article ID code: 50750 Dates: DateEvent2004PublishedSubjects: Science > Mathematics > Electronic computers. Computer science Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 10 Dec 2014 13:52 Last modified: 08 Apr 2024 21:51 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/50750
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