10 citations · 21 across the 6 of their papers we have counts for
14 papers
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…
On simplicial and cubical complexes with short links
Michel Deza, Mathieu Dutour, Mikhail Shtogrin
We consider closed simplicial and cubical -complexes in terms of link of their -faces. Especially, we consider the case, when this link has size 3 or 4, i.e., every $(n-2…
Once more about the 52 four-dimensional parallelotopes
Michel Deza, Viacheslav Grishukhin
There are several works \cite{De} (and \cite{St}), \cite{En}, \cite{Co} and \cite{Va} enumerating four-dimensional parallelotopes. In this work we give a new enumeration showing th…
Properties of parallelotopes equivalent to Voronoi's conjecture
Michel Deza, Viacheslav Grishukhin
A parallelotope is a polytope whose translation copies fill space without gaps and intersections by interior points. Voronoi conjectured that each parallelotope is an affine image…