Enumeration of interval-closed sets via Motzkin paths and quarter-plane walks

2024/12/20 by Elizalde, Sergi, Lafrenière, Nadia, Lewis, Joel Brewster +3
#05A15 #06A07 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.16368

Abstract

We find a generating function for interval-closed sets of the product of two chains poset by constructing a bijection to certain bicolored Motzkin paths. We also find a functional equation for the generating function of interval-closed sets of truncated rectangle posets, including the type A root poset, by constructing a bijection to certain quarter-plane walks.

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