
Counting Lattice Paths Using Fourier Methods
Birkhäuser (Publisher)
1st Edition
Published on 31. August 2019
Book
Paperback/Softback
XII, 136 pages
978-3-030-26695-0 (ISBN)
Description
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.
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.
More details
Series
Edition
1st ed. 2019
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
59 s/w Abbildungen, 1 farbige Abbildung
XII, 136 p. 60 illus., 1 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 9 mm
Weight
236 gr
ISBN-13
978-3-030-26695-0 (9783030266950)
DOI
10.1007/978-3-030-26696-7
Schweitzer Classification
Other editions
Additional editions

Shaun Ault | Charles Kicey
Counting Lattice Paths Using Fourier Methods
E-Book
08/2019
1st Edition
Birkhäuser
€74.89
Available for download
Content
Lattice Paths and Corridors.- One-Dimensional Lattice Walks.- Lattice Walks in Higher Dimensions.- Corridor State Space.- Review: Complex Numbers.- Triangular Lattices.- Selected Solutions.- Index.