A collaborative research group between the MATHEXP Team at Inria Saclay and Simon Fraser University.
Our research program is located at the interface of computer algebra and combinatorics, with a goal of mutually developing strengths, ultimately creating new tools for combinatorics and inspiring algorithmic problems for computer algebra. Leveraging recent advances in algorithms for differential equations and recurrences, we can compute values expressed as scalar products of symmetric functions. Our approach permits enumerative analysis of combinatorial classes bearing a certain regularity structure, following the prototype of $k$-regular graphs. Our primary objective is to determine the differential equations satisfied by generating functions of different generalisations: bipartite graphs, hypergraphs, composite structures, Young tableaux, Latin squares, etc. A conjecture that we will attack concerns the differential transcendence of the generating function of the full set of regular graphs: with this problem, we will in fact seek to identify combinatorial hallmarks of differential transcendence. Other works will concern identities satisfied by the Kronecker product operation in the theory of symmetric functions, which is related to scalar product and is central to the theory of representations. Our general approach to regularity extends to such identities.
Members from the MATHEXP team at Inria Saclay:
Members from Simon Fraser University: