Convex lattice polygonal lines with a constrained number of vertices
Julien Bureaux (MODAL'X), Nathana\"el Enriquez (MODAL'X, LPMA)
TL;DR
This paper provides a combinatorial analysis of convex lattice polygonal lines with a fixed number of vertices, addressing an open question about the existence of a limit shape under such constraints.
Contribution
It introduces a detailed combinatorial framework that confirms the existence of a limit shape for convex lattice polygonal lines with constrained vertices.
Findings
Established the existence of a limit shape under vertex constraints
Developed a combinatorial approach to analyze convex lattice polygons
Answered an open question posed by Vershik
Abstract
A detailed combinatorial analysis of planar convex lattice 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.
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Taxonomy
TopicsDigital Image Processing Techniques · Point processes and geometric inequalities · Mathematics and Applications