$P$-strict promotion and $B$-bounded rowmotion, with applications to tableaux of many flavors

Abstract

We define \(P\)-strict labelings for a finite poset \(P\) as a generalization of semistandard Young tableaux and show that promotion on these objects is in equivariant bijection with a toggle action on \(B\)-bounded \(Q\)-partitions of an associated poset \(Q\). In many nice cases, this toggle action is conjugate to rowmotion. We apply this result to flagged tableaux, Gelfand--Tsetlin patterns, and symplectic tableaux, obtaining new cyclic sieving and homomesy conjectures. We also show \(P\)-strict promotion can be equivalently defined using Bender--Knuth and jeu de taquin perspectives.Mathematics Subject Classifications: 05A19, 05E18