Séminaire Lotharingien de Combinatoire, 95B.74 (2026), 12 pp.
Ben Adenbaum, Spencer Daugherty and Nicholas Mayers
Dimensions of Toggleability Spaces
Abstract.
We establish a conjecture of Defant, Hopkins, Poznanović, and Propp concerning the dimensions of toggleability spaces for products of chains, shifted staircases, type-A root posets, and type-B root posets. Generalizing this result, we show that for a larger family of posets defined by restricted diagrams, the dimensions of toggleability spaces are equal to the rank of the poset plus one. As part of our approach, we build on the technique of rook statistics introduced by Chan, Haddadan, Hopkins, and Moci.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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