Lattice Path Combinatorics
July 11-29, 2016
The theme of counting lattice paths in cones has boomed over the past decade. This interest is due to many reasons. First, many combinatorial objects are in bijection with lattice paths in cones. Furthermore, the mathematical study of lattice paths is very rich, in that it uses various tools, from representation theory of Lie groups and algebras, to complex analysis, analytic/bijective/enumerative combinatorics, probability theory, etc. Researches conducted until now were mainly focused on the case of walks with small steps in the quarter plane, see for instance [1, 2, 3, 5, 7]. These results describe the behavior of generating functions that count such walks, both qualitatively (algebraic/holonomic nature) and quantitatively (exact/asymptotic expressions). Although there are still open questions even within this framework, the research is now moving towards new directions, such as the study of walks with longer steps [6], or in higher dimensions [4]. Many aspects remain to be explored.


Alin Bostan (Inria Saclay)
Kilian Raschel (CNRS & Université de Tours)