Counting Lattice Paths Using Fourier Methods

Language: English

Published by Springer, 2019

3030266958 / 9783030266950

Series: Book 80 of 88 - Applied and Numerical Harmonic Analysis

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Zustand: Hervorragend | Sprache: Englisch | Produktart: Bücher | 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.

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Title
Counting Lattice Paths Using Fourier Methods
Author
Ault, Shaun
Publisher
Springer
Publication year
2019
Condition
Hervorragend
Binding
Soft cover
Language
English
ISBN 10
3030266958
ISBN 13
9783030266950
Series
Book 80 of 88: Applied and Numerical Harmonic Analysis
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Buchpark

Trebbin, Germany

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