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arXiv · 2412.16368

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

Sergi Elizalde·Nadia Lafrenière·Joel Brewster Lewis·Erin McNicholas·Jessica Striker·Amanda Welch
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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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Sergi Elizalde, Nadia Lafrenière, Joel Brewster Lewis, Erin McNicholas, Jessica Striker, Amanda Welch. 2024-12-20. Enumeration of interval-closed sets via Motzkin paths and quarter-plane walks. https://arxiv.org/abs/2412.16368

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