Bijections between Variants of Dyck Paths and Integer Compositions
Abstract
We give bijective results between several variants of lattice paths of length $2n$ (or $2n-2$) 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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.16404
- arXiv:
- arXiv:2406.16404
- Bibcode:
- 2024arXiv240616404G
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Number Theory;
- G.2.1
- E-Print:
- 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