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arXiv · 2607.14028

Cyclic Sieving for Staircase Plane Partitions via Crystals and Electrical Networks

Sam Hopkins·Jesse Kim·Stephan Pfannerer
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Abstract

We prove a cyclic sieving result for the action of promotion on the staircase plane partitions of height two. Our proof has two major algebraic inputs: an interpretation of this promotion action in terms of tensor powers of the spin crystal that was recently studied by Pappe--Pfannerer--Schilling--Simone, and the bush basis of the degree two part of the coordinate ring of the space of electrical networks that was recently introduced by Gao--Lam--Xu. Moreover, we explain how the existence of an electrical canonical basis in all degrees would yield cyclic sieving for promotion of staircase plane partitions of all heights.

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Sam Hopkins, Jesse Kim, Stephan Pfannerer. 2026-07-15. Cyclic Sieving for Staircase Plane Partitions via Crystals and Electrical Networks. https://arxiv.org/abs/2607.14028

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