For each integer partition q with d parts, we denote by Δ (1,q) the lattice simplex obtained as the convex hull in Rd of the standard basis vectors along with the vector - q. For q with two distinct parts such that Δ (1,q) is reflexive and has the integer decomposition property, we establish a characterization of the lattice points contained in Δ (1,q). We then construct a Gröbner basis with a squarefree initial ideal of the toric ideal defined by these simplices. This establishes the existence of a regular unimodular triangulation for reflexive 2-supported Δ (1,q) having the integer decomposition property. As a corollary, we obtain a new proof that these simplices have unimodal Ehrhart h∗-vectors.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics