rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Counting Lattice Paths Using Fourier Methods
  name:
    name part: Ault, Shaun.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Kicey, Charles.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2019
    edition: 1st ed. 2019.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 136 p. 60 illus., 1 illus. in color. online resource.
  abstract: 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.
  table of contents: Lattice Paths and Corridors -- One-Dimensional Lattice Walks -- Lattice Walks in Higher Dimensions -- Corridor State Space -- Review: Complex Numbers -- Triangular Lattices -- Selected Solutions -- Index.
  note: by Shaun Ault, Charles Kicey.
  subject:
    topic: Fourier analysis
  subject:
    topic: Harmonic analysis
  subject:
    topic: Combinatorics
  subject:
    topic: Fourier Analysis
  subject:
    topic: Abstract Harmonic Analysis
  subject:
    topic: Combinatorics
  classification: QA403.5-404.5
  classification: 515.2433
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Applied and Numerical Harmonic Analysis
  identifier: 9783030266967
  identifier: https://doi.org/10.1007/978-3-030-26696-7
  record info:
    record creation date: 190830
    record change date: 20190830132830.0
    record identifier: 978-3-030-26696-7