2018/12/18 by Sebastian Manecke, Manecke, Sebastian, Raman Sanyal +3 · 1 citation
Mathematics · Engineering · Computer Science · #Advanced Combinatorial Mathematics #graph theory and CDMA systems #Advanced Graph Theory Research
paper · pdf · doi:10.48550/arxiv.1812.07491
An S-hypersimplex for S ⊆ \0,1, …,d\ is the convex hull of all 0/1-vectors of length d with coordinate sum in S. These polytopes generalize the classical hypersimplices as well as cubes, crosspolytopes, and halfcubes. In this paper we study faces and dissections of S-hypersimplices. Moreover, we show that monotone path polytopes of S-hypersimplices yield all types of multipermutahedra. In analogy to cubes, we also show that the number of simplices in a pulling triangulation of a halfcube is independent of the pulling order.