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arxiv: 1908.01415 · v2 · pith:XPWZNCRP · submitted 2019-08-04 · math.CO · math.AC· math.AG

Toric ideals of Minkowski sums of unit simplices

Akihiro Higashitani , Hidefumi Ohsugi This is my paper

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classification math.CO math.ACmath.AG
keywords minkowskisimplicesunitsumstoricconjectureidealideals
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In this paper, we discuss the toric ideals of Minkowski sums of unit simplices. More precisely, we prove that the toric ideal of Minkowski sum of unit simplices has a squarefree initial ideal and is generated by quadratic binomials. Moreover, we also prove that Minkowski sums of unit simplices have the integer decomposition property. Those results are a partial contribution to Oda conjecture and B{\o}gvad conjecture.

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