Haar spaces and polynomial selections.
Haar Type Orthonomal Wavelet Bases in R2.
Hajós' theorem and the partition lemma.
Halbierungssätze zur Gestaltabweichung ebener Figuren
Halfspace Range Search: An Algorithmic Application of k-Sets.
Halving point sets.
Hamiltonian Simple Polytopes.
Hamiltonicity and the 3-Opt procedure for the traveling Salesman problem
The 3-Opt procedure deals with interchanging three edges of a tour with three edges not on that tour. For n≥6, the 3-Interchange Graph is a graph on 1/2(n-1)! vertices, corresponding to the hamiltonian tours in K_n; two vertices are adjacent iff the corresponding hamiltonian tours differ in an interchange of 3 edges; i.e. the tours differ in a single 3-Opt step. It is shown that the 3-Interchange Graph is a hamiltonian subgraph of the Symmetric Traveling Salesman Polytope. Upper bounds are derived...
Hard squares with negative activity and rhombus tilings of the plane.
Hard squares with negative activity on cylinders with odd circumference.
Hardness of embedding simplicial complexes in
Let be the following algorithmic problem: Given a finite simplicial complex of dimension at most , does there exist a (piecewise linear) embedding of into ? Known results easily imply polynomiality of (; the case is graph planarity) and of for all . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that and are undecidable for each . Our main result is NP-hardness of and, more generally, of for all , with...
Harmonic sum and duality.
Hearing the shape of a general convex domain: an extension to higher dimensions
Hedgehogs of constant width and equichordal points
We give a characterization of convex hypersurfaces with an equichordal point in terms of hedgehogs of constant width.
Helly property associated with the discrete planes.
Helly-type theorems for infinite and for finite intersections of sets starshaped via staircase paths.
Helly-Type Theorems for Spheres.
Herissons et multiherissons (enveloppes parametrées par leur application de Gauss)
Hidden structures in the class of convex functions and a new duality transform
Our main intention in this paper is to demonstrate how some seemingly purely geometric notions can be presented and understood in an analytic language of inequalities and then, with this understanding, can be defined for classes of functions and reveal new and hidden structures in these classes. One main example which we discovered is a new duality transform for convex non-negative functions on attaining the value 0 at the origin (which we call “geometric convex functions”). This transform, together...
Hierarchical models, marginal polytopes, and linear codes
In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.