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Full-Text Articles in Physical Sciences and Mathematics
Almost Difference Sets And Reversible Divisible Difference Sets, James A. Davis
Almost Difference Sets And Reversible Divisible Difference Sets, James A. Davis
Department of Math & Statistics Faculty Publications
Let G be a group of order mn and N a subgroup of G of order n. If D is a k-subset of G, then D is called a (m, n, k, λ1, λ2) divisible difference set (DDS) provided that the differences dd'-1 for d, d' ∈ D, d ≠ d' contain every nonidentity element of N exactly λ1 times and every element of G - N exactly λ2 times. Difference sets are used to generate designs, as described by [4] and [9]. D will be …
Netsim: A Network Performance Simulator, Lewis Barnett Iii
Netsim: A Network Performance Simulator, Lewis Barnett Iii
Department of Math & Statistics Technical Report Series
The performance of computer communication networks is often given only cursory treatment in undergraduate Networking or Computer Communication courses. A simulation package for the investigation of many aspects of Local Area Network (LAN) performance is introduced. Its use as a tool for allowing undergraduate Networking students to investigate the performance of a popular networking system is discussed.
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 …
A Generalization Of Kraemer's Result On Difference Sets, James A. Davis
A Generalization Of Kraemer's Result On Difference Sets, James A. Davis
Department of Math & Statistics Faculty Publications
Kraemer has shown that every abelian group of order 22d+ 2 with exponent less than 22d+ 3 has a difference set. Generalizing this result, we show that any nonabelian group with a central subgroup of size 2d+ 1 together with an exponent-like condition will have a difference set.
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.