M\'enage Numbers and M\'enage Permutations
classification
🧮 math.CO
keywords
enageformulasnumberspermutationsstructurescatalancombinatorialcount
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In this paper, we study the combinatorial structures of straight and ordinary m\'enage permutations. Based on these structures, we prove four formulas. The first two formulas define a relationship between the m\'enage numbers and the Catalan numbers. The other two formulas count the m\'enage permutations by number of cycles.
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