论文标题
循环（V，4,1） - 设计的存在
The existence of cyclic (v,4,1)-designs
论文作者
论文摘要
Even though Peltesohn proved that a cyclic (v,3,1)-design exists if and only if $v\equiv 1,3\pmod{6}$ as early as 1939, the problem of determining the spectrum of cyclic (v,k,1)-designs with k>3 is far from being settled, even for k=4.本文表明，当且仅当$ v \ equiv 1,4 \ pmod {12} $和$ v \ in \ in \ in \ {16,25,28 \} $中时，存在循环（v，4,1）-Design。
Even though Peltesohn proved that a cyclic (v,3,1)-design exists if and only if $v\equiv 1,3\pmod{6}$ as early as 1939, the problem of determining the spectrum of cyclic (v,k,1)-designs with k>3 is far from being settled, even for k=4. This paper shows that a cyclic (v,4,1)-design exists if and only if $v\equiv 1,4\pmod{12}$ and $v\not\in\{16,25,28\}$.
