Séminaire Lotharingien de Combinatoire, 95B.86 (2026), 12 pp.
Anastasia Nathanson
Multipermutohedral Chow Rings
Abstract.
The multipermutohedral Chow ring was introduced in a series of papers by Clader, Damiolini, Eur, Huang, Li, and Ramadas to study moduli spaces with cyclic symmetry. It generalizes Chow rings of permutohedral varieties and type-B Coxeter arrangements.
In the present work, we establish the combinatorial structure of the multipermutohedral Chow ring
through an explicit Gröbner basis, yielding a Feichtner-Yuzvinsky-type
monomial basis and a formula for the Hilbert series.
Using this formula, we refine the palindromicity of the Hilbert series.
From a representation-theoretic perspective, we also compute the equivariant Hilbert
series under two natural group actions and construct combinatorial maps that
establish equivariant unimodality and palindromicity.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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