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arXiv · 1812.07491

S-hypersimplices, pulling triangulations, and monotone paths

Sebastian Manecke·Raman Sanyal·Jeonghoon So
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Abstract

An $S$-hypersimplex for $S \subseteq \{0,1, \dots,d\}$ 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.

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Sebastian Manecke, Raman Sanyal, Jeonghoon So. 2019-11-28. S-hypersimplices, pulling triangulations, and monotone paths. https://arxiv.org/abs/1812.07491

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