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.
Revised: 2019-11-29
Accepted: 2020-03-02
Published online: 2020-08-20
Classification: 13P10, 52B20
Keywords: Integer decomposition property, Gröbner basis, Generalized permutohedron.
@article{ALCO_2020__3_4_831_0, author = {Higashitani, Akihiro and Ohsugi, Hidefumi}, title = {Toric ideals of Minkowski sums of unit simplices}, journal = {Algebraic Combinatorics}, pages = {831--837}, publisher = {MathOA foundation}, volume = {3}, number = {4}, year = {2020}, doi = {10.5802/alco.117}, language = {en}, url = {alco.centre-mersenne.org/item/ALCO_2020__3_4_831_0/} }
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/item/ALCO_2020__3_4_831_0/
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