Counting semiregular permutations which are products of a full cycle and an involution
David M. Jackson · Transactions of the American Mathematical Society · 1988
Character theoretic methods and the group algebra of the symmetric group are used to derive properties of the number of permutations, with only p p -cycles, for an arbitrary but fixed p p , which are expressible as the product of a full cycle and a fixed point free involution. This problem has application to single face embeddings of p p -regular graphs on surfaces of given genus.