David R Stone- PhD
- Professor at Georgia Southern University
David R Stone
- PhD
- Professor at Georgia Southern University
About
3
Publications
246
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17
Citations
Introduction
Skills and Expertise
Current institution
Additional affiliations
August 1968 - February 2016
Publications
Publications (3)
E. Lucas showed that every point in the plane whose coordinates are consecutive Fibonacci numbers lies on one of two hyperbolas. We show that every point in any fixed higher dimension whose coordinates are consecutive Fibonacci numbers also lies on one of two hyperbolae; moreover, these are the only lattice points on the hyperbolas. We also give so...
Using elementary methods, we derive formulae for the shifted summations Σj=0d-1 Fn+j Fm+j, Σj=0d-1 Ln+j Lm+j and Σj=0d-1 Fn+j Lm+j and the shifted convolutions Σj=0d-1 Fn+j F d-m-j, Σj=0d-1 Ln+j L d-m-j, and Σj=0d-1 Fn+j L d-m-j for positive integers d and arbitrary integers n and m.
We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1kn. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes.
