Counting Lattice Paths Using Fourier Methods Paperback / softback
by Shaun Ault, Charles Kicey
Part of the Lecture Notes in Applied and Numerical Harmonic Analysis series
Paperback / softback
Description
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.
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:136 pages, 1 Illustrations, color; 59 Illustrations, black and white; XII, 136 p. 60 illus., 1 illus
- Publisher:Springer Nature Switzerland AG
- Publication Date:31/08/2019
- Category:
- ISBN:9783030266950
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:136 pages, 1 Illustrations, color; 59 Illustrations, black and white; XII, 136 p. 60 illus., 1 illus
- Publisher:Springer Nature Switzerland AG
- Publication Date:31/08/2019
- Category:
- ISBN:9783030266950
