Difference Sets in a Finite Group

Squares and Difference Sets in Finite Fields

For infinitely many primes p = 4k+1 we give a slightly improved upper bound for the maximal cardinality of a set B ⊂ Zp such that the difference set B−B contains only quadratic residues. Namely, instead of the ”trivial” bound |B| ≤ √p we prove |B| ≤ √ p − 1, under suitable conditions on p. The new bound is valid for approximately three quarters of the primes p = 4k + 1.

Finite Projective Plane Geometries and Difference Sets

On non-Abelian group difference sets

This paper is motivated by R. H. Bruck’s paper[3], in which he proved that the existence of cyclic projective plane of order n ≡ 1 (mod 3) implies that of a non-planar difference set of the same order by proving that such a cyclic projective plane admits a regular non-Abelian automorphism group using n as a multiplier. In this paper we will discuss in detail the possibility of using multipliers...

Lie Group Stability of Finite Difference Schemes

Differential equations arising in fluid mechanics are usually derived from the intrinsic properties of mechanical systems, in the form of conservation laws, and bear symmetries, which are not generally preserved by a finite difference approximation, and leading to inaccurate numerical results. This paper proposes a method that enables us to build a scheme that preserves some of those symmetries.

A Brief Survey of Difference Sets, Partial Difference Sets, and Relative Difference Sets

Difference sets, partial difference sets, and relative difference sets are algebraic structures with combinatorial applications. The purpose of this paper is to give the reader definitions and basic examples of these sets, as well describe their connections to some other well-known combinatorial objects. We will conclude with some examples that illustrate how character theory can be used to pro...