ALGEBRAIC COMBINATORICS

no. 4
Toric ideals of Minkowski sums of unit simplices
Higashitani, Akihiro1; Ohsugi, Hidefumi2
1 Osaka University Graduate School of Information Science and Technology Department of Pure and Applied Mathematics Suita, Osaka 565-0871, Japan
2 Kwansei Gakuin University School of Science and Technology Department of Mathematical Sciences Sanda, Hyogo 669-1337, Japan
Algebraic Combinatorics, Volume 3 (2020) no. 4, pp. 831-837.

In this paper, we discuss the toric ideals of the Minkowski sums of unit simplices. More precisely, we prove that the toric ideal of the Minkowski sum of unit simplices has a squarefree initial ideal and is generated by quadratic binomials. Moreover, we also prove that the Minkowski sums of unit simplices have the integer decomposition property. Those results are a partial contribution to Oda conjecture and Bøgvad conjecture.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.117
Classification: 13P10, 52B20
Keywords: Integer decomposition property, Gröbner basis, Generalized permutohedron.
Higashitani, Akihiro 1; Ohsugi, Hidefumi 2

1 Osaka University Graduate School of Information Science and Technology Department of Pure and Applied Mathematics Suita, Osaka 565-0871, Japan
2 Kwansei Gakuin University School of Science and Technology Department of Mathematical Sciences Sanda, Hyogo 669-1337, Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Higashitani, Akihiro; Ohsugi, Hidefumi. Toric ideals of Minkowski sums of unit simplices. Algebraic Combinatorics, Volume 3 (2020) no. 4, pp. 831-837. doi : 10.5802/alco.117. https://alco.centre-mersenne.org/articles/10.5802/alco.117/

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