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Mathematics > Combinatorics

arXiv:1812.07491 (math)
[Submitted on 18 Dec 2018 (v1), last revised 28 Nov 2019 (this version, v2)]

Title:S-hypersimplices, pulling triangulations, and monotone paths

Authors: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.
Comments: 10 pages, 1 figure; v2: minor changes
Subjects: Combinatorics (math.CO); Metric Geometry (math.MG)
Cite as: arXiv:1812.07491 [math.CO]
  (or arXiv:1812.07491v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1812.07491

Submission history

From: Raman Sanyal [view email]
[v1] Tue, 18 Dec 2018 17:19:24 UTC (16 KB)
[v2] Thu, 28 Nov 2019 12:06:29 UTC (16 KB)
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