arXiv subjects

Francois Hennecart

Publications and source records attributed to Francois Hennecart.

5 recordsLinked to original sources

arXiv2025

Kneser's theorem for upper Buck density and relative results

Kneser's theorem in the integers asserts that denoting by $ \underline{\mathrm{d}}$ the lower asymptotic density, if $\underline{\mathrm{d}}(X_1+\cdots+X_k)<\sum_{i=1}^k\underline{\mathrm{d}}(X_i)$ then the sumset $X_1+\cdots+X_k$ is \emph{periodic} for some positive integer $q$. In this article we establish a similar statement for upper Buck density and compare it with the corresponding result due to Jin involving upper Banach density. We also provide the construction of sequences verifying counterintuitive properties with respect to Buck density of a sequence $A$ and its sumset $A+A$.

math.NT↗

arXiv2024

The Berge-Füredi conjecture on the chromatic index of hypergraphs with large hyperedges

This paper is concerned with two conjectures which are intimately related. The first is a generalization to hypergraphs of Vizing's Theorem on the chromatic index of a graph and the second is the well-known conjecture of Erdős, Faber and Lovász which deals with the problem of coloring a family of cliques intersecting in at most one vertex. We are led to study a special class of uniform and linear hypergraphs for which a number of properties are established.

math.CO↗

arXiv2019

On sum-product bases

Besides various asymptotic results on the concept of sum-product bases in $\mathbb{N}_0$, we consider by probabilistic arguments the existence of thin sets $A,A'$ of integers such that $AA+A=\mathbb{N}_0$ and $A'A'+A'A'=\mathbb{N}_0$.

math.NT↗

arXiv2012

Distribution of residues in approximate subgroups of $\mathbb{F}_p^*$

We extend a result due to Bourgain on the uniform distribution of residues by proving that subsets of the type $f(I)\cdot H$ is equidistributed (as $p$ tends to infinity) where $f$ is a polynomial, $I$ is an interval of $\Fp$ and $H$ is an approximate subgroup of $\mathbb{F}_p^*$ with size larger than polylogarithmic in $p$.

math.NT↗

arXiv2010

Iterated compositions of linear operations on sets of positive upper density

Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded coefficients) on sets of integers having a positive upper density.

math.NT↗