$P$-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.

arXiv comment39 pages, 14 figures

References in corpus (6)

• Resonance in orbits of plane partitions and increasing tableaux
• Proofs and generalizations of a homomesy conjecture of Propp and Roby
• Cyclic Sieving for Plane Partitions and Symmetry
• Rowmotion and Increasing Labeling Promotion
• Minuscule doppelgängers, the coincidental down-degree expectations property, and rowmotion
• Hook-content formulae for symplectic and orthogonal tableaux

Cited by in corpus (5)

• Homomesy via Toggleability Statistics
• Order polynomial product formulas and poset dynamics
• A cyclic sieving phenomenon for symplectic tableaux
• Rowmotion Markov Chains
• $P$-strict promotion and $Q$-partition rowmotion: the graded case