Counting Lattice Paths Using Fourier Methods (Applied And Numerical Harmonic Analysis)
Birkhäuser
ISBN13:
9783030266950
$76.99
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.
- | Author: Shaun Ault, Charles Kicey
- | Publisher: Birkhäuser
- | Publication Date: Aug 31, 2019
- | Number of Pages: 148 pages
- | Language: English
- | Binding: Paperback
- | ISBN-10: 3030266958
- | ISBN-13: 9783030266950
- Author:
- Shaun Ault, Charles Kicey
- Publisher:
- Birkhäuser
- Publication Date:
- Aug 31, 2019
- Number of pages:
- 148 pages
- Language:
- English
- Binding:
- Paperback
- ISBN-10:
- 3030266958
- ISBN-13:
- 9783030266950