Bases for permutation groups and matroids

P. J. Cameron*, D. G. Fon-Der-Flaass

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

In this paper, we give two equivalent conditions for the irredundant bases of a permutation group to be the bases of a matroid. (These are deduced from a more general result for families of sets.) If they hold, then the group acts geometrically on the matroid, in the sense that the fixed points of any element form a flat. Some partial results towards a classification of such permutation groups are given. Further, if G acts geometrically on a perfect matroid design, there is a formula for the number of G-orbits on bases in terms of the cardinalities of flats and the numbers of G-orbits on tuples. This reduces, in a particular case, to the inversion formula for Stirling numbers.

Original languageEnglish
Pages (from-to)537-544
Number of pages8
JournalEuropean Journal of Combinatorics
Volume16
Issue number6
DOIs
Publication statusPublished - 1 Jan 1995

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