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

2025/05/06 by Lafrenière, Nadia, Lewis, Joel Brewster, McNicholas, Erin +2
#05E15 #06A07 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.04000

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]×[n] and use this understanding to prove a homomesy conjecture from (ELMSW 2024) involving the signed cardinality statistic.

Citations

• Toggling, rowmotion, and homomesy on interval-closed sets
• Semidistrim Lattices
• Distributive lattices and Auslander regular algebras
• Dynamical Combinatorics and Torsion Classes
• Combinatorial, piecewise-linear, and birational homomesy for products of\n two chains
• Homomesy in products of two chains
• A uniform bijection between nonnesting and noncrossing partitions
• Promotion and Evacuation

Related

• Toggling, rowmotion, and homomesy on interval-closed sets
• Homomesy in products of two chains
• Combinatorial, piecewise-linear, and birational homomesy for products of\n two chains
• Paths to Understanding Birational Rowmotion on Products of Two Chains
• Enumeration of interval-closed sets via Motzkin paths and quarter-plane walks