English

Grand Dyck paths with air pockets

Combinatorics 2022-11-10 v1 Discrete Mathematics

Abstract

Grand Dyck paths with air pockets (GDAP) are a generalization of Dyck paths with air pockets by allowing them to go below the xx-axis. We present enumerative results on GDAP (or their prefixes) subject to various restrictions such as maximal/minimal height, ordinate of the last point and particular first return decomposition. In some special cases we give bijections with other known combinatorial classes.

Keywords

Cite

@article{arxiv.2211.04914,
  title  = {Grand Dyck paths with air pockets},
  author = {Jean-Luc Baril and Sergey Kirgizov and Rémi Maréchal and Vincent Vajnovszki},
  journal= {arXiv preprint arXiv:2211.04914},
  year   = {2022}
}

Comments

20 pages, 4 figures

R2 v1 2026-06-28T05:31:06.491Z