Turning cycle restrictions into mesh patterns via Foata's fundamental transformation
Combinatorics
2023-10-26 v2
Abstract
An adjacent -cycle is a natural generalization of an adjacent transposition. We show that the number of adjacent -cycles in a permutation maps to the sum of occurrences of two mesh patterns under Foata's fundamental transformation. As a corollary we resolve Conjecture 3.14 in the paper "From Hertzprung's problem to pattern-rewriting systems" by the first author.
Cite
@article{arxiv.2303.17931,
title = {Turning cycle restrictions into mesh patterns via Foata's fundamental transformation},
author = {Anders Claesson and Henning Ulfarsson},
journal= {arXiv preprint arXiv:2303.17931},
year = {2023}
}