Counting Lattice Paths Using Fourier Methods (eBook)

Shaun Ault, Charles Kicey (Autoren)

eBook Download: PDF

2019 | 1st ed. 2019
XII, 136 Seiten
Springer International Publishing (Verlag)
978-3-030-26696-7 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 30.8.2019
• Reihe/Serie: Applied and Numerical Harmonic Analysis
• Reihe/Serie: Applied and Numerical Harmonic Analysis
• Reihe/Serie: Lecture Notes in 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.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Schlagworte: combinatorics • Complex variables • Corridor Numbers • discrete Fourier transform • Lattice Path
• ISBN-10: 3-030-26696-6 / 3030266966
• ISBN-13: 978-3-030-26696-7 / 9783030266967