Sho Matsumoto ; Jonathan Novak

Unitary Matrix Integrals, Primitive Factorizations, and JucysMurphy Elements
dmtcs:2879 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2010,
DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)

https://doi.org/10.46298/dmtcs.2879
Unitary Matrix Integrals, Primitive Factorizations, and JucysMurphy Elements
Authors: Sho Matsumoto ^{1}; Jonathan Novak ^{2,}^{3}
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Sho Matsumoto;Jonathan Novak
1 Graduate School of Mathematics [Nagoya]
2 Combinatorics and Optimization [Waterloo]
3 Mathematical Sciences Research Institute
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 nonminimal primitive factorizations are presented, and interesting connections with JucysMurphy elements, symmetric group characters, and matrix models are described.
Banica, Teodor; Collins, Benoit; Schlenker, JeanMarc, 2011, On Polynomial Integrals Over The Orthogonal Group, Journal Of Combinatorial Theory, Series A, 118, 3, pp. 778795, 10.1016/j.jcta.2010.11.015.
Goulden, I.P.; GuayPaquet, Mathieu; Novak, Jonathan, 2013, Polynomiality Of Monotone Hurwitz Numbers In Higher Genera, Advances In Mathematics, 238, pp. 123, 10.1016/j.aim.2013.01.012.