grlex

We consider two families of $d$-polytopes defined as convex hulls of initial subsets for the graded lexicographic (grlex) and graded reverse lexicographic (grevlex) orders on $\mathbb{Z}^{d}_{\geq 0}$. Our considerations are motivated by the nice properties of the lex polytopes which were studied in relation to optimization problems. We show that the grlex and grevlex polytopes … Read more