Resonance in orbits of plane partitions

Kevin Dilks (1) , Oliver Pechenik (2) , Jessica Striker (1)

1 Department of Mathematics [Fargo]
2 Department of Mathematics [Urbana]

We introduce a new concept of resonance on discrete dynamical systems. Our main result is an equivariant bijection between plane partitions in a box under rowmotion and increasing tableaux under K-promotion, using a generalization of the equivariance of promotion and rowmotion [J. Striker–N. Williams '12] to higher dimensional lattices. This theorem implies new results for K-promotion and new proofs of previous results on plane partitions.

Domaines: Combinatoire [math.CO]

Kevin Dilks, Oliver Pechenik, Jessica Striker. Resonance in orbits of plane partitions. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6394⟩. ⟨hal-02173383⟩