Counting semiregular permutations which are products of a full cycle and an involution

Jackson, D. M.

doi:10.1090/S0002-9947-1988-0920161-4

Counting semiregular permutations which are products of a full cycle and an involution
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Trans. Amer. Math. Soc. 305 (1988), 317-331 Request permission

Abstract:

Character theoretic methods and the group algebra of the symmetric group are used to derive properties of the number of permutations, with only $p$-cycles, for an arbitrary but fixed $p$, 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 $p$-regular graphs on surfaces of given genus.

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