Journal of the Mathematical Society of Japan

Minkowski sum of polytopes and its normality


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In this paper, we consider the normality or the integer decomposition property (IDP, for short) for Minkowski sums of integral convex polytopes. We discuss some properties on the toric rings associated with Minkowski sums of integral convex polytopes. We also study Minkowski sums of edge polytopes and give a sufficient condition for Minkowski sums of edge polytopes to have IDP.

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J. Math. Soc. Japan Volume 68, Number 3 (2016), 1147-1159.

First available in Project Euclid: 19 July 2016

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Zentralblatt MATH identifier

Primary: 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]
Secondary: 14M25: Toric varieties, Newton polyhedra [See also 52B20] 13F99: None of the above, but in this section

Minkowski sum normal integer decomposition property edge polytope


HIGASHITANI, Akihiro. Minkowski sum of polytopes and its normality. J. Math. Soc. Japan 68 (2016), no. 3, 1147--1159. doi:10.2969/jmsj/06831147.

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