6533b859fe1ef96bd12b6ef2

RESEARCH PRODUCT

Grand Dyck paths with air pockets

Jean-luc BarilSergey KirgizovRémi MaréchalVincent Vajnovszki

subject

FOS: Computer and information sciences[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO][INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Discrete Mathematics (cs.DM)FOS: MathematicsMathematics - CombinatoricsCombinatorics (math.CO)Computer Science - Discrete Mathematics

description

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.

yearjournalcountryeditionlanguage
2022-11-09
http://arxiv.org/abs/2211.04914