English

A Bijection on Bilateral Dyck Paths

Combinatorics 2014-01-27 v3

Abstract

It is known that both the number of Dyck paths with 2n2n steps and kk peaks, and the number of Dyck paths with 2n2n steps and kk steps at odd height follow the Narayana distribution. In this paper we present a bijection which explicitly illustrates this equinumeracy. Moreover, we extend this bijection to bilateral Dyck paths. The restriction to Dyck paths preserves the number of contacts.

Keywords

Cite

@article{arxiv.1208.3061,
  title  = {A Bijection on Bilateral Dyck Paths},
  author = {Paul R. G. Mortimer and Thomas Prellberg},
  journal= {arXiv preprint arXiv:1208.3061},
  year   = {2014}
}

Comments

revised version

R2 v1 2026-06-21T21:50:51.309Z