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arXiv · 2211.04914

Grand Dyck paths with air pockets

Jean-Luc Baril·Sergey Kirgizov·Rémi Maréchal·Vincent Vajnovszki
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Abstract

Grand Dyck paths with air pockets (GDAP) are a generalization of Dyck paths with air pockets by allowing them to go below the $x$-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.

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Jean-Luc Baril, Sergey Kirgizov, Rémi Maréchal, Vincent Vajnovszki. 2022-11-09. Grand Dyck paths with air pockets. https://arxiv.org/abs/2211.04914

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