Résumé : A point from the grid ${\mathbb Z}^d$ is called primitive when its coordinates are relatively prime. In this talk we will examine the question of how many primitive points one can pick, whose first non-zero coordinate is positive, under the constraint that the largest coordinate of their sum is at most a fixed number $k$. We will solve the question exactly for all $k$ and $d$. A number of connections with number theory, geometric combinatorics, and the theory of linear programming will be made explicit along the way.
Dernière modification : Wednesday 12 October 2022 | Contact pour cette page : Cyril.Banderier at lipn.univ-paris13.fr |