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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 Difference Sets with and 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.

#### Linked References

- D. Jungnickel, A. Pott, and K. W. Smith, “Difference sets,” in
*The CRC Handbook of Combinatorial Designs, Preprint*, C. J. Colbourn and J. H. Dinitz, Eds., CRC Press, 2005. - K. T. Arasu, “On Lander's conjecture for the case $\lambda =3,\text{J}$,” in
*Proceedings of the 1st Carbondale Combinatorics Conference*, vol. 1, pp. 5–11, 1987. View at Zentralblatt MATH - K. T. Arasu and S. K. Sehgal, “Non-existence of some difference sets,”
*Journal of Combinatorial Mathematics and Combinatorial Computing*, vol. 32, pp. 207–211, 2000. - L. D. Baumert,
*Cyclic Difference Sets*, vol. 182 of*Lecture Notes in Mathematics*, Springer, Berlin, Germany, 1971. - J. F. Dillon, “Variations on a scheme of McFarland for noncyclic difference sets,”
*Journal of Combinatorial Theory. Series A*, vol. 40, no. 1, pp. 9–21, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. Hall, Jr.,
*Combinatorial Theory*, Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons, New York, NY, USA, 2nd edition, 1986, A Wiley-Interscience Publication. - J. E. Iiams, “Lander's tables are complete,” in
*Difference Sets, Sequences and Their Correlation Properties*, vol. 542, pp. 239–257, Klumer Academic, Dordrecht, The Netherlands, 1999. View at Zentralblatt MATH - Y. J. Ionin and M. S. Shrikhande,
*Combinatorics of Symmetric Designs*, vol. 5 of*New Mathematical Monographs*, Cambridge University Press, Cambridge, UK, 2006. View at Publisher · View at Google Scholar - D. Jungnickel and A. Pott, “Difference sets: an introduction,” in
*Difference Sets, Sequences and Their Correlation Properties*, vol. 542, pp. 259–295, Klumer Academic, Dordrecht, The Netherlands, 1999. View at Zentralblatt MATH - L. E. Kopilovich, “Difference sets in noncyclic abelian groups,”
*Cybernetics*, vol. 25, no. 2, pp. 153–157, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - E. S. Lander,
*Symmetric Designs: An Algebraic Approach*, vol. 74 of*London Mathematical Society Lecture Note Series*, Cambridge University Press, Cambridge, UK, 1983. View at Publisher · View at Google Scholar - A. Pott,
*Finite Geometry and Character Theory*, vol. 1601 of*Lecture Notes in Mathematics*, Springer, Berlin, Germany, 1995. - B. Schmidt, “Cyclotomic integers and finite geometry,”
*Journal of the American Mathematical Society*, vol. 12, no. 4, pp. 929–952, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - R. J. Turyn, “Character sums and difference sets,”
*Pacific Journal of Mathematics*, vol. 15, pp. 319–346, 1965. View at Zentralblatt MATH - M. Hall, Jr., “Cyclic projective planes,”
*Duke Mathematical Journal*, vol. 14, pp. 1079–1090, 1947. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - K. T. Arasu and S. K. Sehgal, “On abelian difference sets,” in
*Algebra: Some Recent Advances*, pp. 1–27, Birkhäuser, Basle, Switzerland, 1999. View at Zentralblatt MATH - D. R. Hughes, “Biplanes and semi-biplanes,” in
*Proceedings of the Australian Conference on Combinatorial Mathematics*, vol. 686 of*Lecture Notes in Mathematics*, pp. 55–58, Springer, Berlin, Germany, 1978. View at Zentralblatt MATH - R. E. Kibler, “A summary of noncyclic difference sets,”
*Journal of Combinatorial Theory. Series A*, vol. 25, no. 1, pp. 62–67, 1978. - A. V. López and M. A. G. Sánchez, “On the existence of abelian difference sets with $100<k\le 150$,”
*Journal of Combinatorial Mathematics and Combinatorial Computing*, vol. 23, pp. 97–112, 1997. View at Zentralblatt MATH - B. Franklin and S. Sam, “Non existence of some cyclic difference sets,” 2007.
- A. S. Osifodunrin, “On the existence of non-abelian (210, 77, 28), (336, 135, 54) and (496, 55,6) difference sets,”
*Discrete Mathematics, Algorithms and Applications*, vol. 3, no. 1, pp. 121–137, 2011. View at Publisher · View at Google Scholar - R. A. Liebler, “The inversion formula,”
*Journal of Combinatorial Mathematics and Combinatorial Computing*, vol. 13, pp. 143–160, 1993. View at Zentralblatt MATH - I. Stewart and D. Tall,
*Algebraic Number Theory and Fermat's Last Theorem*, A K Peters, Natick, Mass, USA, Third edition, 2002. - S. L. Ma, “Planar functions, relative difference sets, and character theory,”
*Journal of Algebra*, vol. 185, no. 2, pp. 342–356, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - S. Lang,
*Algebraic Number Theory*, Addison-Wesley Publishing, Reading, Mass, USA, 1970. - O. Gjoneski, A. S. Osifodunrin, and K. W. Smith, on existence of (176, 50, 14) and (704, 38,2) difference sets, to appear.
- W. Ledermann,
*Introduction to Group Characters*, Cambridge University Press, Cambridge, UK, 1977. - M. Hall, Jr.,
*The theory of Groups*, The Macmillan Company, New York, NY, USA, 1959.