论文信息 - Some counting problems related to permutation groups

Some counting problems related to permutation groups

Abstract 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.

Peter J. Cameron

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