English

Lattice paths with infinitely many down steps -- the negative boundary model

Combinatorics 2021-08-31 v1

Abstract

We consider a variation of Dyck paths, where additionally to steps (1,1)(1,1) and (1,1)(1,-1) down-steps (1,j)(1,-j), for j2j\ge2 are allowed. We give credits to Emeric Deutsch for that. The enumeration of such objects living in a strip is performed. Methods are the kernel method and techniques from linear algebra.

Keywords

Cite

@article{arxiv.2108.12797,
  title  = {Lattice paths with infinitely many down steps -- the negative boundary model},
  author = {Helmut Prodinger},
  journal= {arXiv preprint arXiv:2108.12797},
  year   = {2021}
}

Comments

Very early draft. Suggestions are welcome!

R2 v1 2026-06-24T05:30:06.819Z