Bijections between Variants of Dyck Paths and Integer Compositions

Manosij Ghosh Dastidar; Michael Wallner

doi:10.4204/EPTCS.403.22

paper

Bijections between Variants of Dyck Paths and Integer Compositions

arXiv:2406.16404 · doi:10.4204/EPTCS.403.22

Abstract

We give bijective results between several variants of lattice paths of length $2 n$ (or $2 n - 2$ ) and integer compositions of n, all enumerated by the seemingly innocuous formula $4^{n - 1}$ . These associations lead us to make new connections between these objects, such as congruence results.

In Proceedings GASCom 2024, arXiv:2406.14588. A full version of this paper, containing all proofs and more bijective links, appears at arXiv:2402.17849