A bijection on bilateral Dyck paths

zbMATH Open1296.05100arXiv1208.3061MaRDI QIDQ2876028

Paul R. G. Mortimer, Thomas Prellberg

Publication date: 15 August 2014

Published in: The Australasian Journal of Combinatorics (Search for Journal in Brave)

Abstract: It is known that both the number of Dyck paths with $2n$ steps and $k$ peaks, and the number of Dyck paths with $2n$ steps and $k$ 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.

Full work available at URL: https://arxiv.org/abs/1208.3061

zbMATH Keywords

Narayana distributionequinumeracy

Mathematics Subject Classification ID

Paths and cycles (05C38)

Related Items (7)

Between Broadway and the Hudson: A Bijection of Corridor Paths ⋮ A bijection on Dyck paths and its cycle structure ⋮ A bijective proof of an enumerative property of legal bracketings ⋮ Bijections between Łukasiewicz walks and generalized tandem walks ⋮ A weight-preserving bijection between Schröder paths and Schröder permutations ⋮ A Simple Continuous Bijection from Natural Sequences to Dyadic Sequences ⋮ A bijection between two subfamilies of Motzkin paths

This page was built for publication: A bijection on bilateral Dyck paths

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2876028)