Problems of Separation in Enumerative Combinatorics

The project approaches the problem of developing a (non-trivial) semi-algorithm that takes a rational function r(x,y) and an irreducible polynomial p(x,y) as input and outputs (a description of) all solutions of r(x,y) + q(x,y) p(x,y) = f(x) + g(y) where q(x,y) is a rational function whose denominator is not divisible by p(x,y) and f(x) and g(y) are univariate rational functions. The problem is fundamental for the classification of generating functions of lattice walks restricted to cones. Further applications are: the computation of intersections of fields, which again has applications in computer vision and parameter identifiability of ODE models.