Speaker: David Nguyen

Title: An Introduction to Lattice Path Combinatorics

Abstract: A lattice path is a finite sequence of vectors v=(v_1, v_2, ..., v_n) such that each v_j is in the step set S, where S is a given subset of the square lattice Z^2. The case S={(1,1), (1,-1)} corresponds to the classical Dyck paths, for which many ways of getting explicit formulas involving the Catalan numbers are known. This talk will introduce the audience to the wonderful world of lattice paths combinatorics by exploring in details the specific case S = {(1,-2), (1,-1), (1,1), (1,2)}. In particular, the techniques used will be emphasized, rather than the results of the problem, which find applications in, such as, queuing theory and financial pricing options.