Convex lattice polygonal lines with a constrained number of vertices
  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. 
Julien Bureaux (MODAL'X), Nathana\"el Enriquez (MODAL'X, LPMA)
math.PR