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Abstract: A factorization of a permutation into transpositions is called -primitive- ifits factors are weakly ordered. We discuss the problem of enumerating primitivefactorizations of permutations, and its place in the hierarchy of previouslystudied factorization problems. Several formulas enumerating minimal primitiveand possibly non-minimal primitive factorizations are presented, andinteresting connections with Jucys-Murphy elements, symmetric group characters,and matrix models are described.



Author: Sho Matsumoto, Jonathan Novak

Source: https://arxiv.org/







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