PreprintCC BY 4.0arXiv
A flag refinement of the $ h^* $-formula for the hypersimplices
Abstract
The hypersimplex Δk,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 Δk,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.
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BibTeX
@misc{jiang2026flag,
title = {{A flag refinement of the $ h^* $-formula for the hypersimplices}},
author = {Yuhan Jiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07451},
eprint = {2610.07451},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07451},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A flag refinement of the $ h^* $-formula for the hypersimplices
AU - Yuhan Jiang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07451
UR - https://arxiv.org/abs/2610.07451
AB - 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.
ER -