We prove several colorful generalizations of classical theorems in discrete geometry.
Moreover, the colorful generalization of Kirchberger's theorem gives a generalization of the …

A carousel is a dynamical system that describes the movement of an equilateral linkage in
which the midpoint of each rod travels parallel to it. They are closely related to the floating …

Foundations for the topic of crystallizations are proposed through the more general concept
of colored triangulations. Classic results and techniques of crystallizations are reviewed from …

A k‐graph, H = (V, E), is tight if for every surjective mapping f: V → {1,….k} there exists an
edge α ϵ E sicj tjat f| α is injective. Clearly, 2‐graphs are tight if and only if they are connected. …

We consider nonlinear elliptic systems with Dirichlet boundary condition on a bounded
domain in $\mathbb R^{N}$ which is invariant with respect to the action of some group $G$ of …

In this paper we study the topology of transversals to a family of convex sets as a subset of a
Grassmanian manifold. This topology seems to be ruled by a combinatorial structure which …

Triangular embeddings of complete graphs into surfaces are studied through the notion of
tightness which is a natural combinatorial generalization of connectedness for graphs. By …

The complex conjecture of Stefan Banach states that if V is a Banach space over the complex
numbers where for some n, 1<n<dim(V), all of its n-dimensional subspaces are isometric, …

This is the first of two papers in which we classify the regular projective polyhedra in $ \Bbb
P^3 $ with planar faces. Here, we develop the basic notions; we introduce a new diophantine …

We prove a colorful version of Hadwiger’s transversal line theorem: if a family of colored
and numbered convex sets in the plane has the property that any three differently colored …