A subset $B$ of a group $G$ is called a difference basis of $G$ if each element $g\in G$ can be written as the difference $g=ab^{-1}$ of some elements $a,b\in B$. The smallest cardinality $|B|$ of a difference basis $B\subset G$ is called the difference size of $G$ and is denoted by $Δ[G]$. The fraction $ð[G]:=Δ[G]/{\sqrt{|G|}}$ is called the difference characteristic of $G$. We prove that for every $n\in\mathbb N$ the dihedral group $D_{2n}$ of order $2n$ has the difference characteristic $\sqrt{2}\leð[D_{2n}]\leq\frac{48}{\sqrt{586}}\approx1.983$. Moreover, if $n\ge 2\cdot 10^{15}$, then $ð[D_{2n}]<\frac{4}{\sqrt{6}}\approx1.633$. Also we calculate the difference sizes and characteristics of all dihedral groups of cardinality $\le80$.
Combinatorial transfer: a new method for constructing infinite families of nonabelian difference sets, partial difference sets, and relative difference sets
On minimal product-one sequences of maximal length over Dihedral and Dicyclic groups
设$G$是一个有限群.对于$G$上的序列，我们指的是来自$G$的项的有限无序序列，其中允许重复，并且如果它的项可以被排序使得它们的乘积等于$G$的单位元，则我们说它是乘积1序列。大达文波特常数$\mathsf D (G)$是最小乘积1序列的最大长度，即不能分解为两个非平凡乘积1序列的乘积1序列。给出了二面体群和双循环群上长度为$\mathsf D (G)$的所有极小积1序列的明确刻画。基于这些刻画，我们研究了这些群上的积一序列么半群的长度集的并。
Computation of small reflective and dihedral Ramsey numbers
Faculty of Electronic Engineering, University of Niš（尼什大学电子工程学院）；Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska（普里莫尔斯卡大学数学、自然科学和信息技术学院）
Reed College（里德学院）；University of Michigan（密歇根大学）；Amherst College（阿默斯特学院）；Princeton University（普林斯顿大学）；Williams College（威廉姆斯学院）；University of Wisconsin, Madison（威斯康星大学麦迪逊分校）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
