Factorizations of permutations into star transpositions

Abstract

We give a compact expression for the number of factorizations of any permutation into a minimal number of transpositions of the form $(1i)$. Our result generalizes earlier work of Pak in which substantial restrictions were placed on the permutation being factored.

9 pages, 1 figure

References in corpus (1)

• Transitive powers of Young-Jucys-Murphy elements are central

Cited by in corpus (4)

• Noncommutative Independence from Characters of the Infinite Symmetric Group $s_{\infty }$
• Transitive powers of Young-Jucys-Murphy elements are central
• Task swapping networks in distributed systems
• A central limit theorem for star-generators of $S_{\infty }$, which relates to the law of a GUE matrix