Year: 2025
Type: article
Abstract: We find exact and asymptotic formulas for the number of pairs ( s , z ) of N -cycles s and z such that all cycles of the product s · z have lengths from a given set of integers. We then apply one of these results to prove a surprisingly high lower bound for the number of permutations whose block transposition distance from the identity is at least ( N + 1 ) / 2 .
Source: Algebraic Combinatorics
DOI: 10.5802/alco.449
Authors: Miklós Bóna, Boris Pittel
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4415736000