English

On bijections between 231-avoiding permutations and Dyck paths

Combinatorics 2009-10-02 v3

Abstract

We construct a bijection between 231-avoiding permutations and Dyck paths that sends the sum of the major index and the inverse major index of a 231-avoiding permutation to the major index of the corresponding Dyck path. Furthermore, we relate this bijection to others and exhibit a bistatistic on 231-avoiding permutations which is related to the q,t-Catalan numbers.

Keywords

Cite

@article{arxiv.0803.3706,
  title  = {On bijections between 231-avoiding permutations and Dyck paths},
  author = {Christian Stump},
  journal= {arXiv preprint arXiv:0803.3706},
  year   = {2009}
}

Comments

13 pages, the author is very grateful to Matteo Silimbani for providing a proof of Conjecture 5.10

R2 v1 2026-06-21T10:24:34.615Z