Counting Lattice Paths Using Fourier Methods (Paperback, 1st ed. 2019)

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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Applied and Numerical Harmonic Analysis
Release date:	August 2019
First published:	2019
Authors:	Shaun Ault • Charles Kicey
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	136
Edition:	1st ed. 2019
ISBN-13:	978-3-03-026695-0
Categories:	Books > Science & Mathematics > Mathematics > Combinatorics & graph theory Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Promotions
LSN:	3-03-026695-8
Barcode:	9783030266950

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