Ménage Numbers and Ménage Permutations

preprint2015arXivOpen access

Abstract

In this paper, we study the combinatorial structures of straight and ordinary ménage permutations. Based on these structures, we prove four formulas. The first two formulas define a relationship between the ménage numbers and the Catalan numbers. The other two formulas count the ménage permutations by number of cycles.

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