Invariance of rowmotion for variants of the Tamari lattice

Abstract

We show that the rowmotion operator from dynamical algebraic combinatorics behaves the same on all alt $\nu$-Tamari lattices for a fixed lattice path $\nu$. We use this invariance of rowmotion to establish cyclic sieving and homomesy results for rational Tamari lattices. We also conjecture that this invariance extends to the more general cross Tamari lattices.

40 pages, 32 figures