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" Counting lattice paths using Fourier methods / "
Shaun Ault, Charles Kicey.
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BL
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| Record Number
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862748
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| Main Entry
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Ault, Shaun V.,1979-
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| Title & Author
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Counting lattice paths using Fourier methods /\ Shaun Ault, Charles Kicey.
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| Publication Statement
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Cham :: Birkhäuser,, [2019]
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, ©2019
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| Series Statement
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Applied and numerical harmonic analysis,
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| Page. NO
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1 online resource :: illustrations
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| ISBN
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3030266966
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: 9783030266967
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9783030266950
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; LN-ANHA Series Preface; Preface; Contents; 1 Lattice Paths and Corridors; 1.1 Corridor Paths; 1.2 Corridor Numbers and State Vectors; 1.3 Dyck Paths and Motzkin Paths; 1.4 The Binomial Coefficients and Unbounded Lattices; 1.5 Relationship to Reflection Principle; 1.6 Application: Skewed-Bottom Corridors; 2 One-Dimensional Lattice Walks; 2.1 Reflections and Transitions; 2.2 The Discrete Fourier Transform; 2.3 Computing Vertex Numbers Using the DFT; 2.4 Application: Three-Way Paths; 2.5 Application: Unbounded Corridors; 2.6 Application: Walks in Cycle Graphs
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3 Lattice Walks in Higher Dimensions3.1 Multidimensional Corridors; 3.2 Admissibility and Balanced Transition Operators; 3.3 Fourier Analysis of Multidimensional Corridors; 3.4 Walks Within Corridors with Boundary Identifications; 4 Corridor State Space; 4.1 Vertex States as Vectors; 4.2 Using Eigenvectors to Count Corridor Paths; 4.3 Application: Asymptotic Analysis of Centered Corridors; 4.4 Higher Dimensional Centered Corridors; A Review: Complex Numbers; A.1 Properties of the Complex Numbers; A.2 The Complex Exponential; A.3 Complex Vector Spaces; B Triangular Lattices
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B.1 Triangular Lattices and Triangle GroupsB. 2 Tilings of the Plane and Corridors; B.3 Application: Walks in Low-Dimensional Wedges; Selected Solutions; References; ; Index
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| Subject
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Fourier transformations.
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Lattice paths.
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Fourier transformations.
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Lattice paths.
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| Dewey Classification
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511.3/3
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| LC Classification
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QA171.5.A85 2019eb
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| Added Entry
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Kicey, Charles
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