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

  • Author(s): Bernstein, Joseph;
  • Striker, Jessica;
  • Vorland, Corey
  • et al.

Published Web Location

https://doi.org/10.5070/C61055369Creative Commons 'BY' version 4.0 license
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

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