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Pré-Publication, Document De Travail Année : 2014

Lattice convex chains in the plane

Résumé

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.
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Dates et versions

hal-00122105 , version 1 (26-12-2006)
hal-00122105 , version 2 (22-12-2014)

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Julien Bureaux, Nathanael Enriquez. Lattice convex chains in the plane. 2014. ⟨hal-00122105v2⟩
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