Séminaire Lotharingien de Combinatoire, 93B.77 (2025), 12 pp.
Antoine Abram and Jose Bastidas
The h*-Polynomials of Type C Hypersimplices
Abstract.
We study the Ehrhart theory of hypersimplices of type C, as introduced by Lam and Postnikov for general crystallographic root systems. The h*-polynomials of classical hypersimplices are known to relate to various Eulerian statistics on the symmetric group. In this paper, we introduce a new statistic and partial order on signed permutations, which we use to derive explicit formulas for the h*-polynomials of type C hypersimplices. Additionally, we explore connections with other statistics, including flag-excedances and circular descents, flag-descents, and Coxeter descents.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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