Annular noncrossing permutations and minimal transitive factorizations

Heesung Shin; Jang Soo Kim; Seunghyun Seo

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Annular noncrossing permutations and minimal transitive factorizations

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arxiv 1201.5703 v2 pith:35EAGQJB submitted 2012-01-27 math.CO

Jang Soo Kim , Seunghyun Seo , Heesung Shin This is my paper · ORCID

classification math.CO

keywords annularfactorizationsgouldenminimalnoncrossingnumberpermutationtransitive

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abstract

We give two combinatorial proofs of Goulden and Jackson's formula for the number of minimal transitive factorizations of a permutation when the permutation has two cycles. We use the recent result of Goulden, Nica, and Oancea on the number of maximal chains of annular noncrossing partitions of type $B$.

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