Degrees in random uniform minimal factorizations

2020/12/11 by Bellin, Etienne
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2012.06358

Abstract

We are interested in random uniform minimal factorizations of the n-cycle which are factorizations of (1~2… n) into a product of n-1 transpositions. Our main result is an explicit formula for the joint probability that 1 and 2 appear a given number of times in a uniform minimal factorization. For this purpose, we combine bijections with Cayley trees together with explicit computations of multivariate generating functions.

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