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Interval-closed set rowmotion and homomesy on products of two chains
Published 6 May 2025 in math.CO | (2505.04000v1)
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, Lafreni`ere, 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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