Séminaire Lotharingien de Combinatoire, 95B.13 (2026), 12 pp.
Colin Defant, Melissa Sherman-Bennett, and Nathan Williams
Permutahedron Triangulations via Total Linear Stability and the Dual Braid Group
Abstract.
For each finite Coxeter group W and each standard Coxeter element of W, we construct a triangulation of the W-permutahedron. For particular realizations of the W-permutahedron, we show that this is a regular triangulation induced by a height function coming from the theory of total linear stability for Dynkin quivers. We also explore the combinatorial properties of these triangulations, relating the Bruhat order, the noncrossing partition lattice, and Cambrian congruences.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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