14 citations · 19 across the 11 of their papers we have counts for
13 papers
A lower bound theorem for -polytopes with vertices
Guillermo Pineda-Villavicencio, David Yost
The problem of calculating exact lower bounds for the number of -faces of -polytopes with vertices, for each value of , and characterising the minimisers, has recently…
Lower bound results for conditionally decomposable polytopes
Jie Wang, David Yost
It is possible for a combinatorial type of polytope to have both decomposable and indecomposable realizations; here decomposability is meant with respect to Minkowski addition. Suc…
Minimum number of edges of polytopes with 2d + 2 vertices
Guillermo Pineda-Villavicencio, Julien Ugon, David Yost
We define an analogue of the cube and an analogue of the 5-wedge in higher dimensions, each with vertices and edges. We show that these two are the only minimiser…
Zero Duality Gap in View of Abstract Convexity
Hoa T. Bui, Regina S. Burachik, Alexander Y. Kruger +1
Using tools provided by the theory of abstract convexity, we extend conditions for zero duality gap to the context of nonconvex and nonsmooth optimization. Mimicking the classical…
Schur functions for approximation problems
Nadezda Sukhorukova, Julien Ugon
In this paper we propose a new approach to least squares approximation problems. This approach is based on partitioning and Schur function. The nature of this approach is combinato…
Chebyshev multivariate polynomial approximation and point reduction procedure
Nadezda Sukhorukova, Julien Ugon, David Yost
The theory of Chebyshev (uniform) approximation for univariate polynomial and piecewise polynomial functions has been studied for decades. The optimality conditions are based on th…
The excess degree of a polytope
Guillermo Pineda-Villavicencio, Julien Ugon, David Yost
We define the excess degree of a -polytope as , where and denote the number of vertices and edges, respectively. This parameter measures how mu…
On the reconstruction of polytopes
Joseph Doolittle, Eran Nevo, Guillermo Pineda-Villavicencio +2
Blind and Mani, and later Kalai, showed that the face lattice of a simple polytope is determined by its graph, namely its -skeleton. Call a vertex of a -polytope \emph{nonsim…
Compact convex sets with prescribed facial dimensions
Vera Roshchina, Tian Sang, David Yost
While faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, this is not true for general compact convex sets. We address the qu…
More indecomposable polyhedra
Krzysztof Przesławski, David Yost
We apply combinatorial methods to a geometric problem: the classification of polytopes, in terms of Minkowski decomposability. Various properties of skeletons of polytopes are exhi…
Chebyshev approximation for multivariate functions
Nadezda Sukhorukova, Julien Ugon, David Yost
In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions is ver…
Almost simplicial polytopes I. The lower and upper bound theorems
Eran Nevo, Guillermo Pineda-Villavicencio, Julien Ugon +1
We study -vertex -dimensional polytopes with at most one nonsimplex facet with, say, vertices, called {\it almost simplicial polytopes}. We provide tight lower and uppe…
Lower bound theorems for general polytopes
Guillermo Pineda-Villavicencio, Julien Ugon, David Yost
For a -dimensional polytope with vertices, , we calculate precisely the minimum possible number of -dimensional faces, when or . This conf…