Title: Generating Series and Functional Equations Derived from Hidden Algebraic Structures
Abstract:
Identifying "hidden" algebraic structures can significantly simplify the computation of generating series. In this talk, we view combinatorial objects—such as pattern-avoiding words, permutations, Hamilton paths, and rooted (spanning) trees — as bases for different algebraic structures: including algebras, shuffle algebras, operads, and the recently developed "contractads."
By applying Gröbner basis theory and homological methods to these frameworks, we derive functional equations for generating series that are otherwise difficult to access. I will demonstrate the power of this approach by providing new formulas for the generating series of chromatic polynomials and Hamiltonian paths on complete multipartite graphs.
All technical notions will be explained during the talk. No specific prerequisites are expected.