Every Minkowski sum of unit simplices with nonnegative integer coefficients has the integer decomposition property and a toric ideal generated by quadratic binomials with a squarefree initial ideal.
Cayley sums and Minkowski sums of lattice polytopes
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abstract
In this paper, we discuss the integer decomposition property for Cayley sums and Minkowski sums of lattice polytopes. In fact, we characterize when Cayley sums have the integer decomposition property in terms of Minkowski sums. Moreover, by using this characterization, we consider when Cayley sums and Minkowski sums of $2$-convex-normal lattice polytopes have the integer decomposition property. Finally, we also discuss the level property for Minkowski sums and Cayley sums.
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2019 1verdicts
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Toric ideals of Minkowski sums of unit simplices
Every Minkowski sum of unit simplices with nonnegative integer coefficients has the integer decomposition property and a toric ideal generated by quadratic binomials with a squarefree initial ideal.