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Counting lattice paths using Fourier...

Ault, Shaun.

Counting lattice paths using Fourier methods

Record Type:	Electronic resources : Monograph/item
Title/Author:	Counting lattice paths using Fourier methodsby Shaun Ault, Charles Kicey.
Author:	Ault, Shaun.
other author:	Kicey, Charles.
Published:	Cham :Springer International Publishing :2019.
Description:	xii, 136 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Lattice paths.
Online resource:	https://doi.org/10.1007/978-3-030-26696-7
ISBN:	9783030266967$q(electronic bk.)

Counting lattice paths using Fourier methods
Ault, Shaun.

Counting lattice paths using Fourier methods[electronic resource] /by Shaun Ault, Charles Kicey. - Cham :Springer International Publishing :2019. - xii, 136 p. :ill., digital ;24 cm. - Applied and numerical harmonic analysis. - Applied and numerical harmonic analysis..

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

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.

ISBN: 9783030266967$q(electronic bk.)

Standard No.: 10.1007/978-3-030-26696-7doiSubjects--Topical Terms:

245397
Lattice paths.

LC Class. No.: QA171.5 / .A85 2019

Dewey Class. No.: 511.33

Counting lattice paths using Fourier methods
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245 1 0 $a Counting lattice paths using Fourier methods $h [electronic resource] / $c by Shaun Ault, Charles Kicey.
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505 0 $a Lattice Paths and Corridors -- One-Dimensional Lattice Walks -- Lattice Walks in Higher Dimensions -- Corridor State Space -- Review: Complex Numbers -- Triangular Lattices -- Selected Solutions -- Index.
520 $a 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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