Charles Kicey and Shaun V. Ault (Valdosta, GA)
Abstract
The discrete Fourier transform (DFT) can be used in a novel way to answer certain combinatorial questions. Starting with classical corridor lattice paths (the “one-dimensional” case), and moving to walks in arbitrary dimensions and even triangular lattice paths, we are able to produce explicit, exact formulas for the number of lattice paths under various kinds of restrictions. Both algebraic and geometric properties of the DFT are applied throughout. Moreover, our methods are appropriate for undergraduates and can spur a variety of research project ideas.