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 $m$.

9 pages, 4 figures