AbstractThe existence of a cyclic affine plane implies the existence of a Paley type difference set. We use the existence of this difference set to give the following condition on the existence of cyclic affine planes of order n: If n ≡ 8 mod 16 then n − 1 must be a prime. We discuss the structure of the Paley type difference set constructed from the plane
We construct three infinite families of cyclic difference sets, using monomial hyperovals in a desar...
Let D be an affine difference set of order n in an abelian group G relative to a subgroup N. We den...
AbstractA study is made of two generalizations of affine Hjelmslev planes in which the parallel axio...
AbstractThe existence of a cyclic affine plane implies the existence of a Paley type difference set....
This paper formalizes the method of generating projective planes using difference sets. It establis...
AbstractIn this paper, we prove the following theorem: Suppose there exists a cyclic affine plane of...
AbstractThis paper is motivated by Bruck's paper (1955), in which he proved that the existence of cy...
Let D be an abelian difference set for a projective plane ∏ of order n. Then -D is an oval of ∏. Usi...
Let be an abelian group of order , where are distinct odd prime numbers. In this paper, we prove t...
The Prime Power Conjecture (PPC) states that abelian planar difference sets of order n exist only fo...
Difference systems of sets (DSS) are combinatorial configurations that arise in connection with code...
AbstractMotivated by a question about uniform dessins d’enfants, it is conjectured that every cyclic...
This treatise is concerned with generalizations of the Multiplier Theorem for cyclic difference sets...
AbstractAn explicit formula for the number of finite cyclic projective planes (or planar difference ...
Partial difference sets with parameters (,,,)=(,(−1)/2,(−5)/4,(−1)/4) are called Paley type partial ...
We construct three infinite families of cyclic difference sets, using monomial hyperovals in a desar...
Let D be an affine difference set of order n in an abelian group G relative to a subgroup N. We den...
AbstractA study is made of two generalizations of affine Hjelmslev planes in which the parallel axio...
AbstractThe existence of a cyclic affine plane implies the existence of a Paley type difference set....
This paper formalizes the method of generating projective planes using difference sets. It establis...
AbstractIn this paper, we prove the following theorem: Suppose there exists a cyclic affine plane of...
AbstractThis paper is motivated by Bruck's paper (1955), in which he proved that the existence of cy...
Let D be an abelian difference set for a projective plane ∏ of order n. Then -D is an oval of ∏. Usi...
Let be an abelian group of order , where are distinct odd prime numbers. In this paper, we prove t...
The Prime Power Conjecture (PPC) states that abelian planar difference sets of order n exist only fo...
Difference systems of sets (DSS) are combinatorial configurations that arise in connection with code...
AbstractMotivated by a question about uniform dessins d’enfants, it is conjectured that every cyclic...
This treatise is concerned with generalizations of the Multiplier Theorem for cyclic difference sets...
AbstractAn explicit formula for the number of finite cyclic projective planes (or planar difference ...
Partial difference sets with parameters (,,,)=(,(−1)/2,(−5)/4,(−1)/4) are called Paley type partial ...
We construct three infinite families of cyclic difference sets, using monomial hyperovals in a desar...
Let D be an affine difference set of order n in an abelian group G relative to a subgroup N. We den...
AbstractA study is made of two generalizations of affine Hjelmslev planes in which the parallel axio...
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