5 citations · 10 across the 5 of their papers we have counts for
6 papers
The probability that two random integers are coprime
Julien Bureaux, Nathanaël Enriquez
An equivalence is proven between the Riemann Hypothesis and the speed of convergence to 1/zeta(2) of the probability that two independent random variables following the same geomet…
Convex cones, integral zonotopes, limit shape
Imre Bárány, Julien Bureaux, Ben Lund
This paper is about integral zonotopes. It is proven that large zonotopes in a convex cone have a limit shape, meaning that, after suitable scaling, the overwhelming majority of th…
Convex lattice polygonal lines with a constrained number of vertices
Julien Bureaux, Nathanaël Enriquez
A detailed combinatorial analysis of planar convex lattice polygonal lines is presented. This makes it possible to answer an open question of Vershik regarding the existence of a l…
On the number of lattice convex chains
Julien Bureaux, Nathanaël Enriquez
An asymptotic formula is presented for the number of planar lattice convex polygonal lines joining the origin to a distant point of the diagonal. The formula involves the non-trivi…
Partitions of large unbalanced bipartites
Julien Bureaux
We compute the asymptotic behaviour of the number of partitions of large vectors of in the critical regime and in the subcritic…
Lattice convex chains in the plane
Julien Bureaux, Nathanael Enriquez
A detailed combinatorial analysis of planar lattice convex polygonal lines is presented. This makes it possible to answer an open question of Vershik regarding the existence of a l…