Related papers: Products of Foldable Triangulations
In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal…
The space of unit flows on a finite acyclic directed graph is a lattice polytope called the flow polytope of the graph. Given a bipartite graph $G$ with minimum degree at least two, we construct two associated acyclic directed graphs: the…
It is well-known that the tensor product of two bialgebras constitutes the binary product in the category of cocommutative bialgebras and morphisms of bialgebras between them. In this paper, we extend this result to triangular bialgebras…
In this paper we give several criteria for the edge polytope of a fundamental FHM-graph to possess a regular unimodular triangulation in terms of some simple data of the the graph. We further apply our criteria to several examples of graphs…
The lattice size of a lattice polytope is a geometric invariant which was formally introduced in the context of simplification of the defining equation of an algebraic curve, but appeared implicitly earlier in geometric combinatorics.…
We characterize the polytopes in $\mathbb{R}^d$ (not necessarily convex or connected ones) which multi-tile the space by translations along a given lattice. We also give a necessary and sufficient condition for two polytopes in…
We study the weighted partition function for lozenge tilings, with weights given by multivariate rational functions originally defined by Morales, Pak and Panova (2019) in the context of the factorial Schur functions. We prove that this…
We show the existence of polynomial maps which have a regular bifurcation value, while over a neighbourhood of this value the fibres are connected and diffeomorphic.
Recently, cutting planes derived from maximal lattice-free convex sets have been studied intensively by the integer programming community. An important question in this research area has been to decide whether the closures associated with…
We show that any smooth lattice polytope P with codegree greater or equal than (dim(P)+3)/2 (or equivalently, with degree smaller than dim(P)/2), defines a dual defective projective toric manifold. This implies that P is Q-normal (in the…
We study product sets of finite arithmetic progressions of polynomials over a finite field. We prove a lower bound for the size of the product set, uniform in a wide range of parameters. We apply our results to resolve the function field…
The odd-red bipartite perfect matching problem asks to find a perfect matching containing an odd number of red edges in a given red-blue edge-colored bipartite graph. While this problem lies in $\mathsf{P}$, its polyhedral structure remains…
It will be shown that the toric ring of the chain polytope of a finite partially ordered set is an algebra with straightening laws on a finite distributive lattice. Thus in particular every chain polytope possesses a regular unimodular…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
The aim of this paper is to give a survey of the known results concerning centrally symmetric polytopes, spheres, and manifolds. We further enumerate nearly neighborly centrally symmetric spheres and centrally symmetric products of spheres…
We prove that triangular configurations are plentiful in large subsets of cartesian squares of finite quasirandom groups from classes having the quasirandom ultraproduct property, for example the class of finite simple groups. This is…
The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…
Many polytopes arising in polyhedral combinatorics are linear projections of higher-dimensional polytopes with significantly fewer facets. Such lifts may yield compressed representations of polytopes, which are typically used to construct…
We classify here combinatorially rigid simple polytopes with three facets more than their dimension.
We study a family of polytopes and their duals, that appear in various optimization problems as the unit balls for certain norms. These two families interpolate between the hypercube, the unit ball for the $\infty$-norm, and its dual…