Curious cyclic sieving on increasing tableaux

Abstract

We prove a cyclic sieving result for the set of $3\times k$ packed increasing tableaux with maximum entry $m:=3+k$ under K-promotion. The "curiosity" is that the sieving polynomial arises from the $q$-hook formula for standard tableaux of "toothbrush shape" $(2^3,1^{k-2})$ with $m+1$ boxes, whereas K-promotion here only has order $m$.

arXiv comment9 pages, 4 figures

References in corpus (5)

• Resonance in orbits of plane partitions and increasing tableaux
• Promotion of increasing tableaux: frames and homomesies
• A web basis of invariant polynomials from noncrossing partitions
• Orbits of Plane Partitions of Exceptional Lie Type
• Dynamics of plane partitions: Proof of the Cameron-Fon-Der-Flaass conjecture

Cited by in corpus (1)

• A cyclic sieving phenomenon for symplectic tableaux