论文标题
签名差异集
Signed Difference Sets
论文作者
论文摘要
$（V，k，λ）$差额$ v $中的差异设置为$ \ {d_1，d_2，d_2，\ ldots，d_k \} $ of $ g $的$ g $，这样，$ d = \ sum d = \ sum d_i $ in Group $ \ mathbb {z} [z} [z] $ $ $ n = k-λ$。如果$ d = \ sum s_i d_i $，其中$ s_i \ in \ {\ pm 1 \} $满足相同的方程式，我们将其称为签名的差异集。 这概括了差异集（全部$ s_i = 1 $）和循环体称重矩阵（$ g $循环和$λ= 0 $）。我们将证明还有其他感兴趣的案例，并为它们的存在提供一些结果。
A $(v,k,λ)$ difference set in a group $G$ of order $v$ is a subset $\{d_1, d_2, \ldots,d_k\}$ of $G$ such that $D=\sum d_i$ in the group ring $\mathbb{Z}[G]$ satisfies $$D D^{-1} = n + λG,$$ where $n=k-λ$. If $D=\sum s_i d_i$, where the $s_i \in \{ \pm 1\}$, satisfies the same equation, we will call it a signed difference set. This generalizes both difference sets (all $s_i=1$) and circulant weighing matrices ($G$ cyclic and $λ=0$). We will show that there are other cases of interest, and give some results on their existence.
