Counting Lattice Paths Using Fourier Methods [[electronic resource] /] / by Shaun Ault, Charles Kicey
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| Autore: |
Ault Shaun
|
| Titolo: |
Counting Lattice Paths Using Fourier Methods [[electronic resource] /] / by Shaun Ault, Charles Kicey
|
| Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2019 |
| Edizione: | 1st ed. 2019. |
| Descrizione fisica: | 1 online resource (142 pages) |
| Disciplina: | 515.723 |
| Soggetto topico: | Fourier analysis |
| Harmonic analysis | |
| Combinatorics | |
| Fourier Analysis | |
| Abstract Harmonic Analysis | |
| Persona (resp. second.): | KiceyCharles |
| Nota di contenuto: | Lattice Paths and Corridors -- One-Dimensional Lattice Walks -- Lattice Walks in Higher Dimensions -- Corridor State Space -- Review: Complex Numbers -- Triangular Lattices -- Selected Solutions -- Index. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Counting Lattice Paths Using Fourier Methods |
| ISBN: | 3-030-26696-6 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910349321803321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Lecture Notes in Applied and Numerical Harmonic Analysis, . 2512-6482