Some counting problems related to permutation groups

Some counting problems related to permutation groups

1 'I count a lot of things that there's no need to count,' Cameron said. 'Just because that's the way I am. But I count all the things that need to be counted.' A relational structure M consists of a set X and a family of relations on X. The age of M is the class of finite relational structures (in the same language) embeddable in M.

Counting problems from infinite permutation groups

Some counting problems related topermutation

This paper discusses investigations of sequences of natural numbers which count the orbits of an innnite 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 a...

Some measures of finite groups related to permutation bases

I define three “measures” of the complicatedness of a finite group in terms of bases in permutation representations of the group, and consider their relationships to other measures.

Cardinal invariants related to permutation groups

We consider the possible cardinalities of the following three cardinal invariants which are related to the permutation group on the set of natural numbers: ag := the least cardinal number of maximal cofinitary permutation groups; ap := the least cardinal number of maximal almost disjoint permutation families; c(Sym(N)) := the cofinality of the permutation group on the set of natural numbers. We...