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Counting Lattice Paths Using Fourier Methods

Af: Charles Kicey, Shaun Ault Engelsk Paperback
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kr 150

Counting Lattice Paths Using Fourier Methods

Af: Charles Kicey, Shaun Ault Engelsk Paperback
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.
Produktdetaljer
Sprog: Engelsk
Sider: 136
ISBN-13: 9783030266950
Indbinding: Paperback
Udgave:
ISBN-10: 3030266958
Udg. Dato: 31 aug 2019
Længde: 0mm
Bredde: 235mm
Højde: 155mm
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


Sprog Engelsk


Indbinding Paperback


Sider 136


Udgave


Længde 0mm


Bredde 235mm


Højde 155mm


Udg. Dato 31 aug 2019


Oplagsdato 31 aug 2019

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