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PreprintarXiv licencearXiv

Bounded powers of edge ideals: Nearly Gorenstein polytopes

  • Takayuki Hibi
  • Seyed Amin Seyed Fakhari
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Abstract

A lattice polytope 𝒫 βŠ‚ ℝn of dimension n is called nearly Gorenstein if 𝒫 is normal and if its Ehrhart ring is a nearly Gorenstein ring. We study nearly Gorenstein polytopes arising from discrete polymatroids of bounded powers of edge ideals. Especially, it is shown that every nearly Gorenstein polytope coming from either a complete graph or a complete bipartite graph is level.

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Cite

BibTeXRIS
BibTeX
@misc{hibi2026bounded,
  title = {{Bounded powers of edge ideals: Nearly Gorenstein polytopes}},
  author = {Takayuki Hibi and Seyed Amin Seyed Fakhari},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24438},
  eprint = {2610.24438},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24438},
}
RIS
TY  - UNPB
TI  - Bounded powers of edge ideals: Nearly Gorenstein polytopes
AU  - Takayuki Hibi
AU  - Seyed Amin Seyed Fakhari
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24438
UR  - https://arxiv.org/abs/2610.24438
AB  - A lattice polytope 𝒫 βŠ‚ ℝ^n of dimension n is called nearly Gorenstein if 𝒫 is normal and if its Ehrhart ring is a nearly Gorenstein ring. We study nearly Gorenstein polytopes arising from discrete polymatroids of bounded powers of edge ideals. Especially, it is shown that every nearly Gorenstein polytope coming from either a complete graph or a complete bipartite graph is level.
ER  -