# ALGEBRAIC COMBINATORICS

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.

Revised:
Accepted:
Published online:
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},
pages = {831--837},
publisher = {MathOA foundation},
volume = {3},
number = {4},
year = {2020},
doi = {10.5802/alco.117},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.117/}
}
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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