Primitive factorizations, Jucys-Murphy elements, and matrix models

Details Primitive factorizations, Jucys-Murphy elements, and matrix models Primitive factorizations, Jucys-Murphy elements, and matrix models

2010-05-02

arxiv.org/abs/1005.0151v1

Mathematics

Combinatorics

14 pages, FPSAC 2010 conference contribution

Scientific paper

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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