| Autor: |
Sainose, Ichiro, Hamano, Ginji, Emura, Tatsuo, Hibi, Takayuki |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Australasian J. Combin. 85 (2023), 159--163 |
| Druh dokumentu: |
Working Paper |
| Popis: |
Let $\mathcal{P} \subset \mathbb{R}^d$ be a lattice polytope of dimension $d$. Let $b$ denote the number of lattice points belonging to the boundary of $\mathcal{P}$ and $c$ that to the interior of $\mathcal{P}$. It follows from a lower bound theorem of Ehrhart polynomials that, when $c > 0$, the volume of $\mathcal{P}$ is bigger than or equal to $(dc + (d-1)b - d^2 + 2)/d!$. In the present paper, via triangulations, a short and elementary proof of the minimal volume formula is given. |
| Databáze: |
arXiv |
| Externí odkaz: |
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