Geodesic
Minimal transitive factorizations of a permutation of type (p,q)
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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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. 
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     author = {Kim, Jang Soo and Seo, Seunghyun and Shin, Heesung},
     title = {Minimal transitive factorizations of a permutation of type (p,q)},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
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     doi = {10.46298/dmtcs.3073},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3073/}
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Kim, Jang Soo; Seo, Seunghyun; Shin, Heesung. Minimal transitive factorizations of a permutation of type (p,q). Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3073. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3073/

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