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

Published 20 Dec 2024 in math.CO | (2412.16368v1)

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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