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＜E-Book＞
Counting Lattice Paths Using Fourier Methods / by Shaun Ault, Charles Kicey
(Lecture Notes in Applied and Numerical Harmonic Analysis. ISSN:25127209)

Edition	1st ed. 2019.
Publisher	(Cham : Springer International Publishing : Imprint: Birkhäuser)
Year	2019
Language	English
Size	XII, 136 p. 60 illus., 1 illus. in color : online resource
Authors	*Ault, Shaun author Kicey, Charles author SpringerLink (Online service)
Subjects	LCSH:Fourier analysis LCSH:Harmonic analysis LCSH:Discrete mathematics FREE:Fourier Analysis FREE:Abstract Harmonic Analysis FREE:Discrete Mathematics
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-030-26696-7

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