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 language | English |
|---|---|
| Pages (from-to) | 130-137 |
| Number of pages | 8 |
| Journal | Experimental Mathematics |
| Volume | 26 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2017 |
| MoE publication type | A1 Journal article-refereed |
Keywords
- normal polytope
- very ample polytope
- graph polytope
- Hilbert basis
- gap vector
- segmental fibration
- CONVEX POLYTOPES
- TORIC IDEALS