ABSTRACT
We answer several questions posed by Beck, Cox, Delgado, Gubeladze, Haase, Hibi, Higashitani, and Maclagan in [CitationCox et al. 14, Question 3.5 (1),(2), Question 3.6], [CitationBeck et al. 15, Conjecture 3.5(a),(b)], and [CitationHasse 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.
Acknowledgments
We would like to thank Professor Winfried Bruns for help with computations.
Funding
The research was supported by Polish National Science Centre Grant No. 2012/05/D/ST1/01063 and by Swiss National Science Foundation Grants 200020-144531 and 200021-137574. The article was completed during Michał Lasoń’s stay at Freie Universität Berlin in the frame of Polish Ministry “Mobilność Plus” program.