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Original Articles

Non-Normal Very Ample Polytopes – Constructions and Examples

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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.

2000 AMS SUBJECT CLASSIFICATION:

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.

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