### The Combinatorics of Interval Vector Polytopes

#### Abstract

An *interval vector* is a $(0,1)$-vector in $\mathbb{R}^n$ for which all the $1$'s appear consecutively, and an *interval vector polytope* is the convex hull of a set of interval vectors in $\mathbb{R}^n$. We study three particular classes of interval vector polytopes which exhibit interesting geometric-combinatorial structures; e.g., one class has volumes equal to the Catalan numbers, whereas another class has face numbers given by the Pascal 3-triangle.

#### Keywords

Interval vector; lattice polytope; Ehrhart polynomial; root polytope; Catalan number; $f$-vector