Abstract: I will be presenting my work (along with some joint work with Doron Zeilberger) on
how to use symbolic computation to study the area under generalized Dyck paths
(i.e. paths in the xy-plane from the origin to (n,0) with an arbitrary set of atomic steps and
that never go below the x-axis).
Abstract: I will be giving a talk on my joint paper with Robert Dougherty-Bliss,
"Enumerating Restricted Dyck Paths with Context-Free Grammars." The number of Dyck paths of
semilength n is famously C_n, the nth Catalan number. This fact follows after noticing that every
Dyck path can be uniquely parsed according to a context-free grammar. Doron Zeilberger showed that many
restricted sets of Dyck paths satisfy different, more complicated grammars, and from this derived
various generating function identities. We take this further, highlighting some combinatorial results
about Dyck paths obtained via grammatical proof and generalizing some of Zeilbergerâ€™s grammars to infinite families.