An algebraically derived q-analogue of a character sum associated with a class of semiregular permutations (Q810510)

A permutation in which all the cycles have the same length p is called p- semiregular permutation. In this paper the authors derive q-analogues for the number e(k,p) of p-semiregular permutations with k cycles, which are the product of a specified full-cycle and a fixed point free involution by using basic results from hypergeometric series. Such permutations arise in numerous areas of combinatorics.