English

A bijection for length-$5$ patterns in permutations

Combinatorics 2022-12-23 v2

Abstract

A bijection between (31245,32145,31254,32154)(31245,32145,31254,32154)-avoiding permutations and (31425,32415,31524,32514)(31425,32415,31524,32514)-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.

Keywords

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

R2 v1 2026-06-28T05:44:56.982Z