Classically, connectivity is a topological notion for sets, often introduced by means of arcs. A non topological axiomatics has been proposed by Matheron and Serra. The present pa...
Given an integer n 2, and a non-negative integer k, consider all affine hyperplanes in Rn of the form xi = xj +r for i, j [n] and a non-negative integer r k. Let n,k be the pos...
The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into packings with pairwise different widths. Several...
Orthogonal surfaces are nice mathematical objects which have interesting connections to various fields, e.g., integer programming, monomial ideals and order dimension. While orthog...
We construct a new 2-parameter family Emn, m, n 3, of self-dual 2-simple and 2-simplicial 4-polytopes, with flexible geometric realisations. E44 is the 24-cell. For large m, n the...