Grand Dyck paths with air pockets

11/09/2022

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by   Jean-Luc Baril, et al.

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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.