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• W2952337401 abstract "Two factorizations of a permutation into products of cycles are equivalent if one can be obtained from the other by repeatedly interchanging adjacent disjoint factors. This paper studies the enumeration of equivalence classes under this relation. We obtain closed form expressions for generating series of inequivalent minimal transitive factorizations of permutations having up to three cycles, and also of permutations with four cycles when factors are restricted to be transpositions. Our derivations rely on a new correspondence between inequivalent factorizations and acyclic alternating digraphs. Strong similarities between the enumerative results derived here and analogous ones for ordinary factorizations suggest that a unified theory remains to be discovered. We also establish connections between inequivalent factorizations and other well-studied classes of permutation factorizations. In particular, a relationship with monotone factorizations allows us to recover an exact counting formula for the latter due to Goulden, Guay-Paquet and Novak." @default.
• W2952337401 created "2019-06-27" @default.
• W2952337401 creator A5001276084 @default.
• W2952337401 creator A5028480531 @default.
• W2952337401 date "2014-05-20" @default.
• W2952337401 modified "2023-09-27" @default.
• W2952337401 title "Inequivalent Factorizations of Permutations" @default.
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• W2952337401 hasPublicationYear "2014" @default.
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