The Electronic Journal of Combinatorics
An interval vector is a (0,1)" vector in Rn" for which all the 1's appear consecutively, and an interval vector polytope is the convex hull of a set of interval vectors in Rn" Rn. 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.
Beck, Matthias; De Silva, Jessica; Dorfsman-Hopkins, Gabriel; Pruitt, Joseph; and Ruiz, Amanda, "The Combinatorics of Interval Vector Polytopes" (2013). Open Dartmouth: Faculty Open Access Articles. 3394.