Lattice convex chains in the plane
Year: 2006
Type: preprint
Abstract: 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 limit shape when the number of vertices is constrained. The method which is used emphasizes the connection of the combinatorial analysis with the zeros of the zeta function. It is shown how the Riemann Hypothesis leads to an asymptotic equivalent of the number of convex chains.
Source: arXiv (Cornell University)
Authors: Bureaux, Julien, Enriquez, Nathanael
Institution: Modélisation aléatoire de Paris Nanterre
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4299359265