Combinatorial Theory

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