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You searched IISERK - Absolut Unveràˆnderliche.
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Call Number
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515.2433
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Author
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Ault, Shaun. author.
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Title
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Counting Lattice Paths Using Fourier Methods [electronic resource] / by Shaun Ault, Charles Kicey.
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Material Info.
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XII, 136 p. 60 illus., 1 illus. in color. online resource.
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Series
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Lecture Notes in Applied and Numerical Harmonic Analysis, 2512-6482
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Series
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Lecture Notes in Applied and Numerical Harmonic Analysis, 2512-6482
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Summary Note
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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.
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Notes
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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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ISBN
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9783030266967
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Subject
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Fourier analysis.
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Subject
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Harmonic analysis.
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Subject
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combinatorics.
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Subject
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Fourier analysis.
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Subject
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Abstract Harmonic Analysis.
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Subject
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combinatorics.
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Added Entry
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Kicey, Charles. author.
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Added Entry
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SpringerLink (Online service)
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Date
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Year, Month, Day:02102251
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