Journal of the Mathematical Society of Japan

Minkowski sum of polytopes and its normality

Akihiro HIGASHITANI

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 19 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1468956163

Digital Object Identifier
doi:10.2969/jmsj/06831147

Mathematical Reviews number (MathSciNet)
MR3523542

Zentralblatt MATH identifier
06642408

Subjects
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

Keywords
Minkowski sum normal integer decomposition property edge polytope

Citation

HIGASHITANI, Akihiro. Minkowski sum of polytopes and its normality. J. Math. Soc. Japan 68 (2016), no. 3, 1147--1159. doi:10.2969/jmsj/06831147. https://projecteuclid.org/euclid.jmsj/1468956163.


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