# Toric ideals of Minkowski sums of unit simplices

## TL;DR

This paper investigates the algebraic and combinatorial properties of Minkowski sums of unit simplices, showing they have squarefree initial ideals, are generated by quadratic binomials, and possess the integer decomposition property, contributing to longstanding conjectures.

## Contribution

It proves that Minkowski sums of unit simplices have squarefree initial ideals, are generated by quadratic binomials, and have the integer decomposition property, advancing understanding of related conjectures.

## Key findings

- Toric ideals have squarefree initial ideals.
- Generated by quadratic binomials.
- Minkowski sums have the integer decomposition property.

## Abstract

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