Counting Lattice Paths Using Fourier Methods

Released on by Shaun Ault
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  • Counting Lattice Paths Using Fourier Methods Book Detail

  • Author : Shaun Ault
  • Release Date : 2019-08-30
  • Publisher : Springer Nature
  • Genre : Mathematics
  • Pages : 136
  • ISBN 13 : 3030266966
  • File Size : 99,99 MB
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Counting Lattice Paths Using Fourier Methods by Shaun Ault PDF Summary

Book Description: 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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Lattice Path Counting and Applications

Lattice Path Counting and Applications

File Size : 43,43 MB
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Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Lattice Path Counting and Applications focuses on the principles, methodologies,