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Asymptotic Enumeration of Difference Matrices over Cyclic Groups

Published online by Cambridge University Press:  01 August 2017

AARON M. MONTGOMERY
AARON M. MONTGOMERY*
Affiliation:
Department of Mathematics, Baldwin Wallace University, Berea, Ohio, 44017, USA (e-mail: amontgom@bw.edu)
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Abstract

We identify a relationship between a certain family of random walks on Euclidean lattices and difference matrices over cyclic groups. We then use the techniques of Fourier analysis to estimate the return probabilities of these random walks, which in turn yields the asymptotic number of difference matrices over cyclic groups as the number of columns increases.

Keywords

Primary 05B20Secondary 05A16

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Issue 1 , January 2018 , pp. 84 - 109
Copyright
Copyright © Cambridge University Press 2017 

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