论文标题
在完美的序列覆盖阵列上
On Perfect Sequence Covering Arrays
论文作者
论文摘要
psca $（v，t，λ）$是$ v $ - 元素字母$ \ \ {0，\ dots，v-1 \} $的多种排列，因此，$ t $ t $不同的字母元素的每个序列都以准确的$λ$的排列方式出现在指定的顺序中。对于$ v \ geq t \ geq 2 $，我们将$ g（v，t）$定义为最小的正整数$λ$，以使PSCA $（V，V，T，λ）$。我们表明$ g（6，3）= g（7，3）= g（7，4）= 2 $和$ g（8，3）= 3 $。使用组的合适置换表示，我们对$ g（v，t）$的上限进行改进，以$ v \ leq 32 $和$ 3 \ le t \ le 6 $的许多值。我们还证明了对PSCA列之间符号分布的许多限制。
A PSCA$(v, t, λ)$ is a multiset of permutations of the $v$-element alphabet $\{0, \dots, v-1\}$ such that every sequence of $t$ distinct elements of the alphabet appears in the specified order in exactly $λ$ of the permutations. For $v \geq t \geq 2$, we define $g(v, t)$ to be the smallest positive integer $λ$ such that a PSCA$(v, t, λ)$ exists. We show that $g(6, 3) = g(7, 3) = g(7, 4) = 2$ and $g(8, 3) = 3$. Using suitable permutation representations of groups we make improvements to the upper bounds on $g(v, t)$ for many values of $v \leq 32$ and $3\le t\le 6$. We also prove a number of restrictions on the distribution of symbols among the columns of a PSCA.
