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Lattice convex chains in the plane

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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00122105
Contributor : Nathanael Enriquez <>
Submitted on : Monday, December 22, 2014 - 5:40:35 PM
Last modification on : Friday, March 27, 2020 - 3:00:58 AM
Document(s) archivé(s) le : Monday, March 23, 2015 - 7:45:34 PM

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

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