Ault / Kicey Counting Lattice Paths Using Fourier Methods

1. Auflage 2019
ISBN: 978-3-030-26696-7
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 136 Seiten

Reihe: Mathematics and Statistics (R0)

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 to higher-dimensional lattice path problems with ease. The technique is carefully developed in the first three chapters using the algebraic properties of the DFT, moving from one-dimensional problems to higher dimensions. In the following chapter, the discussion turns to geometric properties of the DFT in order to study the corridor state space. Each chapter poses open-ended questions and exercises to prompt further practice and future research. Two appendices are also provided, which cover complex variables and non-rectangular lattices, thus ensuring the text will be self-contained and serve as a valued reference.
Counting Lattice Paths Using Fourier Methods is ideal for upper-undergraduates and graduate students studying combinatorics or other areas of mathematics, as well as computer science or physics. Instructors will also find this a valuable resource for use in their seminars. Readers should have a firm understanding of calculus, including integration, sequences, and series, as well as a familiarity with proofs and elementary linear algebra.

Zielgruppe

Research

Autoren/Hrsg.

Ault, Shaun

Kicey, Charles

Inhaltsverzeichnis

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