Special subsets of difference sets with particular emphasis on skew Hadamard difference sets |
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Authors: | Robert S Coulter Todd Gutekunst |
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Institution: | (1) Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA;(2) Department of Mathematics, King’s College, Wilkes-Barre, PA 18711, USA |
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Abstract: | This article introduces a new approach to studying difference sets via their additive properties. We introduce the concept
of special subsets, which are interesting combinatorial objects in their own right, but also provide a mechanism for measuring
additive regularity. Skew Hadamard difference sets are given special attention, and the structure of their special subsets
leads to several results on multipliers, including a categorisation of the full multiplier group of an abelian skew Hadamard
difference set. We also count the number of ways to write elements as a product of any number of elements of a skew Hadamard
difference set.
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Keywords: | Difference sets Skew Hadamard difference sets Additive regularity |
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