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ISRN Algebra
Volume 2012 (2012), Article ID 367129, 19 pages
http://dx.doi.org/10.5402/2012/367129
Research Article

On the Existence of ( 𝑣 , π‘˜ , πœ† ) Difference Sets with π‘˜ < 1 2 5 0 and π‘˜ βˆ’ πœ† Is a Square

Division of Sciences and Mathematics, Department of Mathematics, Livingstone College, Salisbury, NC 28144, USA

Received 20 January 2012; Accepted 8 February 2012

Academic Editors: A. V. Kelarev, D. Kressner, H. You, and A. Zimmermann

Copyright © 2012 Adegoke Solomon Osifodunrin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We combine Turyn's self-conjugacy result, variance technique, Dillon dihedral trick, and Sylow theorem to investigate the existence of ( 𝑣 , π‘˜ , πœ† ) difference sets in which π‘˜ βˆ’ πœ† is a square and π‘˜ < 1 2 5 0 .