On a generalization of a theorem by Vosper.
New bounds for codes identifying vertices in graphs.
Large sets with small doubling modulo are well covered by an arithmetic progression
We prove that there is a small but fixed positive integer such that for every prime larger than a fixed integer, every subset of the integers modulo which satisfies and is contained in an arithmetic progression of length . This is the first result of this nature which places no unnecessary restrictions on the size of .
On the construction of dense lattices with a given automorphisms group
We consider the problem of constructing dense lattices in with a given non trivial automorphisms group. We exhibit a family of such lattices of density at least , which matches, up to a multiplicative constant, the best known density of a lattice packing. For an infinite sequence of dimensions , we exhibit a finite set of lattices that come with an automorphisms group of size , and a constant proportion of which achieves the aforementioned lower bound on the largest packing density. The algorithmic...
On zero-free subset sums
On the critical pair theory in ℤ/pℤ
On some subgroup chains related to Kneser’s theorem
A recent result of Balandraud shows that for every subset of an abelian group there exists a non trivial subgroup such that holds only if . Notice that Kneser’s Theorem only gives . This strong form of Kneser’s theorem follows from some nice properties of a certain poset investigated by Balandraud. We consider an analogous poset for nonabelian groups and, by using classical tools from Additive Number Theory, extend some of the above results. In particular we obtain short proofs...
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