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Exploring The Structure Of Partial Difference Sets With Denniston Parameters, Nicolas Ferree
Exploring The Structure Of Partial Difference Sets With Denniston Parameters, Nicolas Ferree
Honors Theses
In this work, we investigate the structure of particular partial difference sets (PDS) of size 70 with Denniston parameters in an elementary abelian group and in a nonelementary abelian group. We will make extensive use of character theory in our investigation and ultimately seek to understand the nature of difference sets with these parameters. To begin, we will cover some basic definitions and examples of difference sets and partial difference sets. We will then move on to some basic theorems about partial difference sets before introducing a group ring formalism and using it to explore several important constructions of partial …
New Families Of Semi-Regular Relative Difference Sets, James A. Davis, Jonathan Jedwab, Miranda Mowbray
New Families Of Semi-Regular Relative Difference Sets, James A. Davis, Jonathan Jedwab, Miranda Mowbray
Department of Math & Statistics Faculty Publications
We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2. No such RDSs were previously known. We use examples from the first construction to produce semi-regular RDSs in groups whose order can contain more than two distinct prime factors. For u greater than 2 these are the first such RDSs, and for u = 2 we obtain new examples.
Construction Of Relative Difference Sets In P-Groups, James A. Davis
Construction Of Relative Difference Sets In P-Groups, James A. Davis
Department of Math & Statistics Faculty Publications
Jungnickel (1982) and Elliot and Butson (1966) have shown that (pj+1,p,pj+1,pj) relative difference sets exist in the elementary abelian p-group case (p an odd prime) and many 2-groups for the case p = 2. This paper provides two new constructions of relative difference sets with these parameters; the first handles any p-group (including non-abelian) with a special subgroup if j is odd, and any 2-group with that subgroup if j is even. The second construction shows that if j is odd, every abelian group …
An Exponent Bound For Relative Difference Sets In P-Groups, James A. Davis
An Exponent Bound For Relative Difference Sets In P-Groups, James A. Davis
Department of Math & Statistics Faculty Publications
An exponent bound is presented for abelian (pi+j, pi, pi+j, pi) relative difference sets: this bound can be met for i≤j.
A Note On Intersection Numbers Of Difference Sets, K. T. Arasu, James A. Davis, Dieter Jungnickel, Alexander Pott
A Note On Intersection Numbers Of Difference Sets, K. T. Arasu, James A. Davis, Dieter Jungnickel, Alexander Pott
Department of Math & Statistics Faculty Publications
We present a condition on the intersection numbers of difference sets which follows from a result of Jungnickel and Pott [3]. We apply this condition to rule out several putative (non-abelian) difference sets and to correct erroneous proofs of Lander [4] for the nonexistence of (352, 27, 2)- and (122, 37, 12)-difference sets.