scholarly journals Difference sets and computability theory

1998 ◽  
Vol 93 (1-3) ◽  
pp. 63-72
Author(s):  
Rod Downey ◽  
Zoltán Füredi ◽  
Carl G. Jockusch ◽  
Lee A. Rubel
Keyword(s):  
Difference Sets ◽  
Computability Theory

scholarly journals On non-symmetric relative difference sets

2008 ◽  
Vol 37 (3) ◽  
pp. 427-435 ◽  
Author(s):  
Yutaka HIRAMINE
Keyword(s):  
Difference Sets ◽  
Relative Difference ◽  
Relative Difference Sets

scholarly journals Graphs of vectorial plateaued functions as difference sets

2021 ◽  
Vol 71 ◽  
pp. 101795
Author(s):  
Ayça Çeşmelioğlu ◽  
Oktay Olmez
Keyword(s):  
Difference Sets ◽  
Plateaued Functions

Divisible Semiplanes, Arcs, and Relative Difference Sets

1987 ◽  
Vol 39 (4) ◽  
pp. 1001-1024 ◽  
Author(s):  
Dieter Jungnickel
Keyword(s):  
Projective Plane ◽  
Difference Sets ◽  
Difference Set ◽  
Relative Difference ◽  
List Type ◽  
Relative Difference Set ◽  
Large Collection ◽  
Baer Subplane ◽  
Relative Difference Sets ◽  
Definition Of

In this paper we shall be concerned with arcs of divisible semiplanes. With one exception, all known divisible semiplanes D (also called “elliptic” semiplanes) arise by omitting the empty set or a Baer subset from a projective plane Π, i.e., D = Π\S, where S is one of the following:(i) S is the empty set.(ii) S consists of a line L with all its points and a point p with all the lines through it.(iii) S is a Baer subplane of Π.We will introduce a definition of “arc” in divisible semiplanes; in the examples just mentioned, arcs of D will be arcs of Π that interact in a prescribed manner with the Baer subset S omitted. The precise definition (to be given in Section 2) is chosen in such a way that divisible semiplanes admitting an abelian Singer group (i.e., a group acting regularly on both points and lines) and then a relative difference set D will always contain a large collection of arcs related to D (to be precise, —D and all its translates will be arcs).

scholarly journals Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets

1999 ◽  
Vol 87 (1) ◽  
pp. 74-119 ◽  
Author(s):  
Ronald Evans ◽  
Henk D.L. Hollmann ◽  
Christian Krattenthaler ◽  
Qing Xiang
Keyword(s):  
Difference Sets ◽  
Gauss Sums ◽  
Cyclic Difference Sets ◽  
Jacobi Sums

Classifying model-theoretic properties

2008 ◽  
Vol 73 (3) ◽  
pp. 885-905 ◽  
Author(s):  
Chris J. Conidis
Keyword(s):  
Model Theory ◽  
Computability Theory ◽  
Prime Model ◽  
Decidable Theory ◽  
Dense Sets ◽  
Equivalent Properties ◽  
The Relationship

AbstractIn 2004 Csima, Hirschfeldt, Knight, and Soare [1] showed that a set A ≤T 0′ is nonlow2 if and only if A is prime bounding, i.e., for every complete atomic decidable theory T, there is a prime model computable in A. The authors presented nine seemingly unrelated predicates of a set A, and showed that they are equivalent for sets. Some of these predicates, such as prime bounding, and others involving equivalence structures and abelian p-groups come from model theory, while others involving meeting dense sets in trees and escaping a given function come from pure computability theory.As predicates of A, the original nine properties are equivalent for sets; however, they are not equivalent in general. This article examines the (degree-theoretic) relationship between the nine properties. We show that the nine properties fall into three classes, each of which consists of several equivalent properties. We also investigate the relationship between the three classes, by determining whether or not any of the predicates in one class implies a predicate in another class.

scholarly journals New Partial Difference Sets in Ztp2 and a Related Problem about Galois Rings

2001 ◽  
Vol 7 (1) ◽  
pp. 165-188 ◽  
Author(s):  
Xiang-Dong Hou ◽  
Ka Hin Leung ◽  
Qing Xiang
Keyword(s):  
Related Problem ◽  
Difference Sets ◽  
Galois Rings ◽  
Partial Difference ◽  
Partial Difference Sets

Relative difference sets in semidirect products with an amalgamated subgroup

2005 ◽  
Vol 13 (3) ◽  
pp. 211-221 ◽  
Author(s):  
John C. Galati ◽  
Alain C. LeBel
Keyword(s):  
Difference Sets ◽  
Relative Difference ◽  
Semidirect Products ◽  
Relative Difference Sets ◽  
Amalgamated Subgroup

On substructures of abelian difference sets with classical parameters

2008 ◽  
Vol 16 (3) ◽  
pp. 182-190
Author(s):  
Kevin Jennings
Keyword(s):  
Difference Sets ◽  
Classical Parameters

scholarly journals Difference Sets and Positive Exponential Sums I. General Properties

2013 ◽  
Vol 20 (1) ◽  
pp. 17-41 ◽  
Author(s):  
Máté Matolcsi ◽  
Imre Z. Ruzsa
Keyword(s):  
Exponential Sums ◽  
Difference Sets ◽  
General Properties
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