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arXiv · 2505.04000

Interval-closed set rowmotion and homomesy on products of two chains

Nadia Lafrenière·Joel Brewster Lewis·Erin McNicholas·Jessica Striker·Amanda Welch
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Abstract

We study rowmotion dynamics on interval-closed sets. Our first main result proves a simplification of the global definition of interval-closed set rowmotion from (Elder, Lafrenière, McNicholas, Striker, and Welch 2024). We then completely describe the orbits of interval-closed set rowmotion on products of two chains $[2]\times[n]$ and use this understanding to prove a homomesy conjecture from (ELMSW 2024) involving the signed cardinality statistic.

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Nadia Lafrenière, Joel Brewster Lewis, Erin McNicholas, Jessica Striker, Amanda Welch. 2025-05-06. Interval-closed set rowmotion and homomesy on products of two chains. https://arxiv.org/abs/2505.04000

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