Abstract:
Functional equations with catalytic variable first appeared in an article by Temperley concerning combinatorial problems in statistical mechanics and in a series of works on map enumeration by Tutte but they also have prominent roles in the enumeration of lattice paths, pattern avoiding permutations, stack-sortable permutations, certain types of polyominoes and various other structures.
In this talk, we take a hands on approach to equations with one catalytic variable and show via several examples how to solve them, compute coefficient asymptotics and statistics of additional counting parameters (e.g. expectation & variance).