Counting Lattice Paths Using Fourier Methods

Shaun Ault, Charles Kicey (Autoren)

Buch | Softcover

XII, 136 Seiten

2019
Springer International Publishing (Verlag)
978-3-030-26695-0 (ISBN)

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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.

Lattice Paths and Corridors.- One-Dimensional Lattice Walks.- Lattice Walks in Higher Dimensions.- Corridor State Space.- Review: Complex Numbers.- Triangular Lattices.- Selected Solutions.- Index.

Erscheinungsdatum	02.09.2019
Reihe/Serie	Applied and Numerical Harmonic Analysis
Reihe/Serie	Lecture Notes in Applied and Numerical Harmonic Analysis
Zusatzinfo	XII, 136 p. 60 illus., 1 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	235 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
Schlagworte	combinatorics • Complex variables • Corridor Numbers • discrete Fourier transform • Lattice Path
ISBN-10	3-030-26695-8 / 3030266958
ISBN-13	978-3-030-26695-0 / 9783030266950
Zustand	Neuware