11 citations · 25 across the 7 of their papers we have counts for
7 papers
On piecewise-linear homeomorphisms between distributive and anti-blocking polyhedra
Christoph Pegel, Raman Sanyal
Stanley (1986) introduced the order polytope and chain polytope of a partially ordered set and showed that they are related by a piecewise-linear homeomorphism. In this paper we vi…
The Minkowski Property and Reflexivity of Marked Poset Polytopes
Xin Fang, Ghislain Fourier, Christoph Pegel
We provide a Minkowski sum decomposition of marked chain-order polytopes into building blocks associated to elementary markings and thus give an explicit minimal set of generators…
Vertex-Maximal Lattice Polytopes Contained in 2-Simplices
Jan-Philipp Litza, Christoph Pegel, Kirsten Schmitz
Motivated by the problem of bounding the number of rays of plane tropical curves we study the following question: Given and a unimodular -simplex what is th…
A Continuous Family of Marked Poset Polytopes
Xin Fang, Ghislain Fourier, Jan-Philipp Litza +1
For any marked poset we define a continuous family of polytopes, parametrized by a hypercube, generalizing the notions of marked order and marked chain polytopes. By providing tran…
The Face Structure and Geometry of Marked Order Polyhedra
Christoph Pegel
We study a class of polyhedra associated to marked posets. Examples of these polyhedra are Gelfand-Tsetlin polytopes and cones, as well as Berenstein-Zelevinsky polytopes, all of w…
Cofibrant objects in the Thomason Model Structure
Roman Bruckner, Christoph Pegel
There are Quillen equivalent Thomason model structures on the category of small categories, the category of small acyclic categories and the category of posets. These share the pro…
Polytopes of eigensteps of finite equal norm tight frames
Tim Haga, Christoph Pegel
Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated f…