Geodesic
Unitary Matrix Integrals, Primitive Factorizations, and Jucys-Murphy Elements
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010).

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A factorization of a permutation into transpositions is called "primitive'' if its factors are weakly ordered.We discuss the problem of enumerating primitive factorizations of permutations, and its place in the hierarchy of previously studied factorization problems. Several formulas enumerating minimal primitive and possibly non-minimal primitive factorizations are presented, and interesting connections with Jucys-Murphy elements, symmetric group characters, and matrix models are described. 
@article{DMTCS_2010_special_259_a74,
     author = {Matsumoto, Sho and Novak, Jonathan},
     title = {Unitary {Matrix} {Integrals,} {Primitive} {Factorizations,} and {Jucys-Murphy} {Elements}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)},
     year = {2010},
     doi = {10.46298/dmtcs.2879},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2879/}
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Matsumoto, Sho; Novak, Jonathan. Unitary Matrix Integrals, Primitive Factorizations, and Jucys-Murphy Elements. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi : 10.46298/dmtcs.2879. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2879/

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