Curious cyclic sieving on increasing tableaux
Christian Gaetz, Oliver Pechenik, Jessica Striker, Joshua P., Swanson

TL;DR
This paper establishes a cyclic sieving phenomenon for a specific set of increasing tableaux under K-promotion, revealing a surprising connection to the q-hook formula for certain standard tableaux shapes.
Contribution
It introduces a new cyclic sieving result for increasing tableaux with a novel link to the q-hook formula for toothbrush-shaped tableaux.
Findings
Cyclic sieving holds for 3 x k increasing tableaux under K-promotion.
The sieving polynomial is derived from the q-hook formula for toothbrush shape tableaux.
K-promotion has order m, matching the maximum entry in the tableaux.
Abstract
We prove a cyclic sieving result for the set of packed increasing tableaux with maximum entry under K-promotion. The "curiosity" is that the sieving polynomial arises from the -hook formula for standard tableaux of "toothbrush shape" with boxes, whereas K-promotion here only has order .
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Mathematical Dynamics and Fractals · Polynomial and algebraic computation
