5 research outputs found
-strict promotion and -bounded rowmotion, with applications to tableaux of many flavors
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.Comment: 39 pages, 14 figure