On the number of lattice convex chains

Julien Bureaux (1) , Nathanaël Enriquez (2, 1)

1 MODAL'X - Modélisation aléatoire de Paris X
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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-trivial zeroes of the zeta function and leads to a necessary and sufficient condition for the Riemann Hypothesis to hold.

Mots clés: polyominoes; local limit theorem; convex polygons; grand canonical ensemble; zeta functions

Domaines: Probabilités [math.PR]; Combinatoire [math.CO]

Julien Bureaux, Nathanaël Enriquez. On the number of lattice convex chains. 2016. ⟨hal-01292817⟩