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Algorithms for Computing the Lattice Size
Harrison, Anthony Westbrook

2018, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Science.
The lattice size of a lattice polygon P with respect to a set XRn, denoted lsX(P), is the smallest positive integer d such that the image of P under an affine unimodular transformation T is contained within the d-dilate of X. This problem is closely related to toric geometry and has applications to coding theory. Previously known algorithms to calculate this parameter required the enumeration of lattice points, a computationally expensive procedure. We have developed an algorithm that needs only the vertices of P when X is the unit square. We also give similarly efficient algorithms for the case when X is the unit cube (in three-dimensions) or the standard 2-simplex.
Jenya Soprunova (Advisor)
Ivan Soprunov (Advisor)
Mark Lewis (Committee Member)
Mikhail Chebotar (Committee Member)
Feodor Dragan (Committee Member)
Austin Melton (Committee Member)
48 p.

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Harrison, A. (2018). Algorithms for Computing the Lattice Size. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Harrison, Anthony. "Algorithms for Computing the Lattice Size." Electronic Thesis or Dissertation. Kent State University, 2018. OhioLINK Electronic Theses and Dissertations Center. 23 Sep 2018.

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Harrison, Anthony "Algorithms for Computing the Lattice Size." Electronic Thesis or Dissertation. Kent State University, 2018. https://etd.ohiolink.edu/

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