11 citations · 18 across the 6 of their papers we have counts for
6 papers
Families of Equiangular Lines and Lattices
Jacques Martinet
We construct Euclidean lattices whose sets of minimal vectors support some large equiangular families of lines, using notably reduction modulo~ of lattices. %as considered in \c…
Voronoi complexes in higher dimensions, cohomology of for and the triviality of
Mathieu Dutour Sikirić, Philippe Elbaz-Vincent, Alexander Kupers +1
We enumerate the low dimensional cells in the Voronoi cell complexes attached to the modular groups and for , using quotient sublattices techniques…
Hermite versus Minkowski
Jacques Martinet
We compare for an -dimensional Euclidean lattice $\Lb$ the smallest possible values of the product of the norms of ~vectors which either constitute a basis for $\Lb$ (Hermite…
On the index system of well-rounded lattices
Jacques Martinet
Let $\Lb$ be a lattice in an -dimensional Euclidean space and let $\Lb'$ be a Minkowskian sublattice of $\Lb$, that is, a sublattice having a basis made of representatives f…
Bases of minimal vectors in lattices, III
Jacques Martinet, Achill Schürmann
We prove that all Euclidean lattices of dimension which are generated by their minimal vectors, also possess a basis of minimal vectors. By providing a new counterexample,…
On classifying Minkowskian sublattices
Wolfgang Keller, Jacques Martinet, Achill Schürmann
Let be a lattice in an -dimensional Euclidean space and let be a Minkowskian sublattice of , that is, a sublattice having a basis made of representatives for the…