Some counting problems related to permutation groups

Peter J. Cameron*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


This paper discusses investigations of sequences of natural numbers which count the orbits of an infinite permutation group on n-sets or n-tuples. It surveys known results on the growth rates, cycle index techniques, and an interpretation as the Hilbert series of a graded algebra, with a possible application to the question of smoothness of growth. I suggest that these orbit-counting sequences are sufficiently special to be interesting but sufficiently common to support a general theory.

Original languageEnglish
Pages (from-to)77-92
Number of pages16
JournalDiscrete Mathematics
Issue number1-3
Publication statusPublished - 28 Oct 2000


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