A bijection for length-$5$ patterns in permutations
Combinatorics
2022-12-23 v2
Abstract
A bijection between -avoiding permutations and -avoiding permutations is constructed, which preserves five classical set-valued statistics. Combining with two codings of permutations due respectively to Baril--Vajnovszki and Martinez--Savage proves an enumerative conjecture posed by Gao and Kitaev. Moreover, the generating function for the common counting sequence is proved to be algebraic.
Cite
@article{arxiv.2211.06871,
title = {A bijection for length-$5$ patterns in permutations},
author = {Joanna N. Chen and Zhicong Lin},
journal= {arXiv preprint arXiv:2211.06871},
year = {2022}
}
Comments
Final remarks are added: 28 pages, 6 figures