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Unitary Matrix Integrals, Primitive Factorizations, and Jucys-Murphy Elements

Abstract : 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.
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Sho Matsumoto, Jonathan Novak. Unitary Matrix Integrals, Primitive Factorizations, and Jucys-Murphy Elements. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.403-412. ⟨hal-01186308⟩

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