Description: Counting Lattice Paths Using Fourier Methods, Paperback by Ault, Shaun; Kicey, Charles, ISBN 3030266958, ISBN-13 9783030266950, Brand New, Free shipping in the US 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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Book Title: Counting Lattice Paths Using Fourier Methods
Number of Pages: Xii, 136 Pages
Publication Name: Counting Lattice Paths Using Fourier Methods
Language: English
Publisher: Springer International Publishing A&G
Subject: Mathematical Analysis, Discrete Mathematics
Publication Year: 2019
Type: Textbook
Item Weight: 16 Oz
Author: Shaun Ault, Charles Kicey
Item Length: 9.3 in
Subject Area: Mathematics
Item Width: 6.1 in
Series: Applied and Numerical Harmonic Analysis Ser.
Format: Trade Paperback
