Year: 2026
Type: preprint
Abstract: The hypersimplex $Δ_{k,n}$ is the convex hull of all 0/1-vectors of length $ n $ with coordinate sum $ k $. Early conjectured, and Kim proved, a combinatorial formula for the $ h^* $-polynomial of $Δ_{k,n}$ in terms of hypersimplicial decorated ordered set partitions. In this paper, we refine the Early--Kim formula to the flag $h$-numbers of the alcove triangulation of $\hyp$. We also give a representation-theoretic interpretation of its flag $f$-numbers in terms of Young permutation modules.
Source: arXiv (Cornell University)
Author: Jiang, Yuhan
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221043188