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, Tome 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.

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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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Higashitani, Akihiro; Ohsugi, Hidefumi. Toric ideals of Minkowski sums of unit simplices. Algebraic Combinatorics, Tome 3 (2020) no. 4, pp. 831-837. doi: 10.5802/alco.117

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