论文标题
完美序列覆盖阵列的多项式结构
A polynomial construction of 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 $不同的字母元素的每个序列都以$λ$排列的方式出现在指定顺序中。对于$ v \ geq t $，让$ g（v，t）$为最小的正整数$λ$，使得存在PSCA $（V，T，λ）$。我们提出了一个明确的结构，该结构证明了$ g（v，t）= o（v^{t（t-2））$，用于固定$ t \ geq 4 $。施工方法涉及对尺寸合适的尺寸的投影空间$ t -2 $的置换表示，并从每个置换中删除所有数量的符号。在这个空间是desarguesian投影平面的情况下，我们还表明，存在该平面的项目群的排列表示，涵盖了其点的绝大多数固定次数的绝大多数次数。
A PSCA$(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 $λ$ permutations. For $v \geq t$, let $g(v, t)$ be the smallest positive integer $λ$ such that a PSCA$(v, t, λ)$ exists. We present an explicit construction that proves $g(v,t) = O(v^{t(t-2)})$ for fixed $t \geq 4$. The method of construction involves taking a permutation representation of the group of projectivities of a suitable projective space of dimension $t - 2$ and deleting all but a certain number of symbols from each permutation. In the case that this space is a Desarguesian projective plane, we also show that there exists a permutation representation of the group of projectivities of the plane that covers the vast majority of 4-sequences of its points a fixed number of times.
