Geodesic
Integer decomposition property of dilated polytopes
David A. Cox1 ; Christian Haase2 ; Takayuki Hibi3 ; Akihiro Higashitani4
1Amherst College
2Freie Universitat Berlin
3Osaka University
4Kyoto University
The electronic journal of combinatorics, Tome 21 (2014) no. 4
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An integral convex polytope $\mathcal{P} \subset \mathbb{R}^N$ possesses the integer decomposition property if, for any integer $k > 0$ and for any $\alpha \in k \mathcal{P} \cap \mathbb{Z}^{N}$, there exist $\alpha_{1}, \ldots, \alpha_k \in \mathcal{P} \cap \mathbb{Z}^{N}$ such that $\alpha = \alpha_{1} + \cdots + \alpha_k$. A fundamental question is to determine the integers $k > 0$ for which the dilated polytope $k\mathcal{P}$ possesses the integer decomposition property. In the present paper, combinatorial invariants related to the integer decomposition property of dilated polytopes will be proposed and studied.
DOI : 10.37236/4204
Classification : 52B20, 14Q15, 14M25
Mots-clés : lattice polytope, integer decomposition property, integrally closed, Ehrhart series, Hilbert basis

David A. Cox  1   ; Christian Haase  2   ; Takayuki Hibi  3   ; Akihiro Higashitani  4

1 Amherst College
2 Freie Universitat Berlin
3 Osaka University
4 Kyoto University 
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     title = {Integer decomposition property of dilated polytopes},
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David A. Cox; Christian Haase; Takayuki Hibi; Akihiro Higashitani. Integer decomposition property of dilated polytopes. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/4204

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