Séminaire Lotharingien de Combinatoire, 95B.2 (2026), 12 pp.
Sam Hopkins, Jesse Kim and Stephan Pfannerer
Cyclic Sieving for Staircase Plane Partitions via Crystals and Electrical Networks
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.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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