2025/04/04 by Abram, Antoine, Bastidas, Jose
#52B20 51F15 06A07 05A05 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2504.03898
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.