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100   $a20190830d2019      u|             0
101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aCounting Lattice Paths Using Fourier Methods$b[electronic resource] /$fby Shaun Ault, Charles Kicey
205   $a1st ed. 2019.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2019.
215   $a1 online resource (142 pages)
225 1 $aLecture Notes in Applied and Numerical Harmonic Analysis,$x2512-6482
311   $a3-030-26695-8 
327   $aLattice Paths and Corridors -- One-Dimensional Lattice Walks -- Lattice Walks in Higher Dimensions -- Corridor State Space -- Review: Complex Numbers -- Triangular Lattices -- Selected Solutions -- Index.
330   $aThis monograph introduces a novel and effective approach to counting lattice paths by using the discrete Fourier transform (DFT) as a type of periodic generating function. Utilizing a previously unexplored connection between combinatorics and Fourier analysis, this method will allow readers to move to higher-dimensional lattice path problems with ease. The technique is carefully developed in the first three chapters using the algebraic properties of the DFT, moving from one-dimensional problems to higher dimensions. In the following chapter, the discussion turns to geometric properties of the DFT in order to study the corridor state space. Each chapter poses open-ended questions and exercises to prompt further practice and future research. Two appendices are also provided, which cover complex variables and non-rectangular lattices, thus ensuring the text will be self-contained and serve as a valued reference. Counting Lattice Paths Using Fourier Methods is ideal for upper-undergraduates and graduate students studying combinatorics or other areas of mathematics, as well as computer science or physics. Instructors will also find this a valuable resource for use in their seminars. Readers should have a firm understanding of calculus, including integration, sequences, and series, as well as a familiarity with proofs and elementary linear algebra.
410  0$aLecture Notes in Applied and Numerical Harmonic Analysis,$x2512-6482
606   $aFourier analysis
606   $aHarmonic analysis
606   $aCombinatorics
606   $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058
606   $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015
606   $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010
615  0$aFourier analysis.
615  0$aHarmonic analysis.
615  0$aCombinatorics.
615 14$aFourier Analysis.
615 24$aAbstract Harmonic Analysis.
615 24$aCombinatorics.
676   $a515.723
700   $aAult$b Shaun$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781302
702   $aKicey$b Charles$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910349321803321
996   $aCounting Lattice Paths Using Fourier Methods$92499262
997   $aUNINA