English

An Upper Bound Theorem concerning lattice polytopes

Combinatorics 2016-10-10 v4 Commutative Algebra Algebraic Geometry

Abstract

R. P. Stanley proved the Upper Bound Conjecture in 1975. We imitate his proof for the Ehrhart rings. We give some upper bounds for the volume of integrally closed lattice polytopes. We derive some inequalities for the delta-vector of integrally closed lattice polytopes. Finally we apply our results for reflexive integrally closed and order polytopes.

Keywords

Cite

@article{arxiv.1103.5895,
  title  = {An Upper Bound Theorem concerning lattice polytopes},
  author = {Gabor Hegedüs},
  journal= {arXiv preprint arXiv:1103.5895},
  year   = {2016}
}

Comments

17 pages, corrected typos

R2 v1 2026-06-21T17:46:56.399Z