Minimal transitive factorizations of a permutation of type (p,q)

Abstract

We give a combinatorial proof 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.

Keywords

• minimal transitive factorizations
• annular noncrossing partitions
• bijective proof
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]