Recurrences, Generating Functions and D-Finiteness: Two (Related) Examples
by Dr Nicholas Beaton
Abstract: I will discuss the enumeration of combinatorial objects via generating functions and functional equations, with a focus on the D-finiteness (or lack thereof) of the functions. This will be explored through two examples, both related to pattern-avoiding permutations. The first is the enumeration of permutations which avoid the consecutive pattern 1423. The second is a family of sequences which generalise the Catalan and Baxter sequences, and their application to parallelogram polyominoes.
This is joint work with Tony Guttmann and Andrew Conway on one hand, and Mathilde Bouvel, Veronica Guerrini and Simone Rinaldi on the other.