English

Bijections between Variants of Dyck Paths and Integer Compositions

Combinatorics 2024-06-25 v1 Number Theory

Abstract

We give bijective results between several variants of lattice paths of length 2n2n (or 2n22n-2) and integer compositions of n, all enumerated by the seemingly innocuous formula 4n14^{n-1}. These associations lead us to make new connections between these objects, such as congruence results.

Keywords

Cite

@article{arxiv.2406.16404,
  title  = {Bijections between Variants of Dyck Paths and Integer Compositions},
  author = {Manosij Ghosh Dastidar and Michael Wallner},
  journal= {arXiv preprint arXiv:2406.16404},
  year   = {2024}
}

Comments

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

R2 v1 2026-06-28T17:16:54.708Z