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Counting Lattice Paths Using Fourier Methods

Af: Charles Kicey, Shaun Ault Engelsk Paperback

Counting Lattice Paths Using Fourier Methods

Af: Charles Kicey, Shaun Ault Engelsk Paperback
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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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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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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 136
ISBN-13: 9783030266950
Indbinding: Paperback
Udgave:
ISBN-10: 3030266958
Kategori: Kompleks analyse, komplekse variabler
Udg. Dato: 31 aug 2019
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 31 aug 2019
Forfatter(e): Charles Kicey, Shaun Ault
Forfatter(e) Charles Kicey, Shaun Ault

Kategori Kompleks analyse, komplekse variabler

ISBN-13 9783030266950

Sprog Engelsk

Indbinding Paperback

Sider 136

Udgave

Længde 0mm

Bredde 155mm

Højde 235mm

Udg. Dato 31 aug 2019

Oplagsdato 31 aug 2019

Forlag Springer Nature Switzerland AG

Kategori sammenhænge