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Discrete Mathematics and Combinatorics Commons™

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1992

Articles 1 - 5 of 5

Full-Text Articles in Discrete Mathematics and Combinatorics

Almost Difference Sets And Reversible Divisible Difference Sets, James A. Davis Dec 1992

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 …

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Another Way Of Counting Nᴺ, Arthur T. Benjamin, Fritz Juhnke Aug 1992

Another Way Of Counting Nᴺ, Arthur T. Benjamin, Fritz Juhnke

All HMC Faculty Publications and Research

An original combinatorial proof of a combinatorial identity is presented.

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Construction Of Relative Difference Sets In P-Groups, James A. Davis May 1992

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 …

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An Exponent Bound For Relative Difference Sets In P-Groups, James A. Davis Jan 1992

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.

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A Theorem On Reproducing Kernel Hilbert Spaces Of Pairs, Daniel Alpay Jan 1992

A Theorem On Reproducing Kernel Hilbert Spaces Of Pairs, Daniel Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we study reproducing kernel Hilbert and Banach spaces of pairs. These are a generalization of reproducing kernel Krein spaces and, roughly speaking, consist of pairs of Hilbert (or Banach) spaces of functions in duality with respect to a sesquilinear form and admitting a left and right reproducing kernel. We first investigate some properties of these spaces of pairs. It is then proved that to every function K(z, ω) analytic in z and ω* there is a neighborhood of the origin that can be associated with a reproducing kernel Hilbert space of pairs with left reproducing kernel K(z, …

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