Counting lattice paths using Fourier methods

著者

    • Ault, Shaun
    • Kicey, Charles

書誌事項

Counting lattice paths using Fourier methods

Shaun Ault, Charles Kicey

(Lecture notes in applied and numerical harmonic analysis / series editor, John J. Benedetto)

Birkhäuser , Springer, c2019

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注記

Includes bibliographical references (p. 131-133) and index

内容説明・目次

内容説明

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.

目次

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

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詳細情報

  • NII書誌ID(NCID)
    BB28937836
  • ISBN
    • 9783030266950
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    [S.l.],Cham
  • ページ数/冊数
    xii, 136 p.
  • 大きさ
    24 cm
  • 親書誌ID
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