Non-Normal Very Ample Polytopes - Constructions and Examples

Michal Lason, Mateusz Michalek

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We answer several questions posed by Beck, Cox, Delgado, Gubeladze, Haase, Hibi, Higashitani, and Maclagan in [Cox et al. 14, Question 3.5 (1),(2), Question 3.6], [Beck et al. 15, Conjecture 3.5(a),(b)], and [Hasse et al. 07, Open question 3 (a),(b) p. 2310, Question p. 2316] by constructing a new family of non-normal very ample polytopes. These polytopes are certain segmental fibrations of unimodular graph polytopes, we explicitly compute their invariants - Hilbert function, Ehrhart polynomial, and gap vector.

Original languageEnglish
Pages (from-to)130-137
Number of pages8
JournalExperimental Mathematics
Volume26
Issue number2
DOIs
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • normal polytope
  • very ample polytope
  • graph polytope
  • Hilbert basis
  • gap vector
  • segmental fibration
  • CONVEX POLYTOPES
  • TORIC IDEALS

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