2 citations · 4 across the 4 of their papers we have counts for
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Perfect but not generating Delaunay polytopes
Mathieu Dutour Sikiric, Konstantin Rybnikov
In his seminal 1951 paper "Extreme forms" Coxeter \cite{cox51} observed that for one can add vectors to the perfect lattice $\sfA_9$ so that the resulting perfect lattice…
Combinatorial cube packings in cube and torus
Mathieu Dutour Sikirić, Yoshiaki Itoh
We consider sequential random packing of cubes with $z\in \frac{1}{N}\ZZ^n$ into the cube and the torus $\QuotS{\RR^n}{2\ZZ^n}$ as . In the cube c…
Automorphism groups of root systems matroids
Mathieu Dutour Sikiric, Anna Felikson, Pavel Tumarkin
Given a root system , the vector system is obtained by taking a representative in each antipodal pair . The matroid …
The decomposition of the hypermetric cone into L-domains
Mathieu Dutour Sikiric, Viatcheslav Grishukhin
The hypermetric cone $\HYP_{n+1}$ is the parameter space of basic Delaunay polytopes in n-dimensional lattice. The cone $\HYP_{n+1}$ is polyhedral; one way of seeing this is that m…
How to compute the rank of a Delaunay polytope
Mathieu Dutour Sikiric, Viatcheslav Grishukhin
Roughly speaking, the rank of a Delaunay polytope (first introduced in \cite{DGL92}) is its number of degrees of freedom. In \cite{DL}, a method for computing the rank of a Delauna…
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…