Toric ideals of Minkowski sums of unit simplices
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: 2019-08-14
Revised: 2019-11-29
Accepted: 2020-03-02
Published online: 2020-08-20
DOI: https://doi.org/10.5802/alco.117
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},
     publisher = {MathOA foundation},
     volume = {3},
     number = {4},
     year = {2020},
     pages = {831-837},
     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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