Separation probabilities for products of permutations

Abstract

We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements $1,2,...,k$ are in distinct cycles of the random permutation of $\{1,2,...,n\}$ obtained as product of two uniformly random $n$-cycles.

References in corpus (3)

• Explicit monomial expansions of the generating series for connection coefficients
• Bijections and symmetries for the factorizations of the long cycle
• On products of long cycles: short cycle dependence and separation probabilities

Cited by in corpus (5)

• A simple model of trees for unicellular maps
• Expansion of polynomial Lie group integrals in terms of certain maps on surfaces, and factorizations of permutations
• Separation probabilities and analogues of a Zagier-Stanley formula
• On products of long cycles: short cycle dependence and separation probabilities
• On products of permutations with the most uncontaminated cycles by designated labels