Gorenstein simplices with a given δ-polynomial
| Autor: | Akiyoshi Tsuchiya, Takayuki Hibi, Koutarou Yoshida |
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| Rok vydání: | 2019 |
| Předmět: |
Discrete mathematics
Polynomial 52B12 52B20 Open problem Lattice (group) 020206 networking & telecommunications Polytope 0102 computer and information sciences 02 engineering and technology 01 natural sciences Prime (order theory) Theoretical Computer Science Combinatorics Unimodular matrix 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Mathematics - Combinatorics Discrete Mathematics and Combinatorics Equivalence (measure theory) Mathematics |
| Zdroj: | Discrete Mathematics. 342:111619 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/j.disc.2019.111619 |
| Popis: | To classify the lattice polytopes with a given $\delta$-polynomial is an important open problem in Ehrhart theory. A complete classification of the Gorenstein simplices whose normalized volumes are prime integers is known. In particular, their $\delta$-polynomials are of the form $1+t^k+\cdots+t^{(v-1)k}$, where $k$ and $v$ are positive integers. In the present paper, a complete classification of the Gorenstein simplices with the above $\delta$-polynomials will be performed, when $v$ is either $p^2$ or $pq$, where $p$ and $q$ are prime integers with $p \neq q$. Moreover, we consider the number of Gorenstein simplices, up to unimodular equivalence, with the expected $\delta$-polynomial. Comment: 14 pages, to appear in Discrete Mathematics |
| Databáze: | OpenAIRE |
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