Asymptotic Nonexistence of Difference Sets in Dihedral Groups

Asymptotic Nonexistence of Difference Sets in Dihedral Groups

Almost all known results on difference sets need severe restrictions on the parameters. The main purpose of this paper is to provide an asymptotic nonexistence result free from any assumptions on the parameters. The only assumption we make is that the underlying group is dihedral. Difference sets originally mainly were studied in cyclic groups where they exist in abundance. For example, for any...

Difference Bases in Dihedral Groups

A subset B of a group G is called a difference basis of G if each element g ∈ G can be written as the difference g = ab−1 of some elements a, b ∈ B. The smallest cardinality |B| of a difference basis B ⊂ G is called the difference size of G and is denoted by ∆[G]. The fraction ð[G] := ∆[G]/ √ |G| is called the difference characteristic of G. We prove that for every n ∈ N the dihedral group D2n ...

Some nonexistence results on divisible difference sets

Families of 2-critical sets for dihedral groups

The dihedral group is defined by 〈x, y | x = y = e, xy = yx−1〉 for n ≥ 3 and has order 2n. In this note four families of 2-critical sets are presented for the Latin square based on this group for even n.

Calculations of Dihedral Groups Using Circular Indexation

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...