Counting Lattice Paths Using Fourier Methods

• Main Authors: Ault, Shaun (Author, http://id.loc.gov/vocabulary/relators/aut), Kicey, Charles (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2019.
• Edition: 1st ed. 2019.
• Series: Lecture Notes in Applied and Numerical Harmonic Analysis,
• Subjects: Fourier analysis.; Harmonic analysis.; Combinatorics.; Fourier Analysis.; Abstract Harmonic Analysis.

This monograph introduces a novel and effective approach to counting lattice paths by using the discrete Fourier transform (DFT) as a type of periodic generating function. Utilizing a previously unexplored connection between combinatorics and Fourier analysis, this method will allow readers to move...

Table of Contents:

• Lattice Paths and Corridors
• One-Dimensional Lattice Walks
• Lattice Walks in Higher Dimensions
• Corridor State Space
• Review: Complex Numbers
• Triangular Lattices
• Selected Solutions
• Index.