The Combinatorics of Interval Vector Polytopes

  • Matthias Beck
  • Jessica De Silva
  • Gabriel Dorfsman-Hopkins
  • Joseph Pruitt
  • Amanda Ruiz
Keywords: Interval vector, lattice polytope, Ehrhart polynomial, root polytope, Catalan number, $f$-vector


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.

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