10 citations · 29 across the 6 of their papers we have counts for
6 papers
Cube packings, second moment and holes
Mathieu Dutour, Yoshiaki Itoh, Alexei Poyarkov
We consider tilings and packings of $\RR^d$ by integral translates of cubes , which are $4\ZZ^d$-periodic. Such cube packings can be described by cliques of an associated…
Elementary elliptic -polycycles
Michel Deza, Mathieu Dutour, Mikhail Shtogrin
We consider the following generalization of the decomposition theorem for polycycles. A {\em -polycycle} is, roughly, a plane graph, whose faces, besides some disjoint {\em…
Graphs that are isometrically embeddable in hypercubes
Michel Deza, Mathieu Dutour-Sikiric, Sergey Shpectorov
A connected 3-valent plane graph, whose faces are - or 6-gons only, is called a {\em graph }. We classify all graphs , which are isometric subgraphs of a -hypercube…
Zigzag structure of complexes
Michel Deza, Mathieu Dutour
Inspired by Coxeter's notion of Petrie polygon for -polytopes (see \cite{Cox73}), we consider a generalization of the notion of zigzag circuits on complexes and compute the zigz…
Adjacency method for extreme Delaunay polytopes
Mathieu Dutour
The {\em hypermetric cone} is defined as the cone of semimetrics satisfying the {\em hypermetric inequalities}. Every {\em Delaunay polytope} corresponds to a ray of this polyhedra…
Some six-dimensional rigid forms
Mathieu Dutour, Frank Vallentin
One can always decompose Dirichlet-Voronoi polytopes of lattices non-trivially into a Minkowski sum of Dirichlet-Voronoi polytopes of rigid lattices. In this report we show how one…