论文标题
最低肯德尔$τ$的置换代码大小的新界限三个
New Bounds on the Size of Permutation Codes With Minimum Kendall $τ$-distance of Three
论文作者
论文摘要
我们研究$ p（n，3）$，是所有排列的最大子集的大小$ s_n $，最低kendall $τ$ -Distance $ 3 $。通过组合小组理论和整数编程，我们将$ p（p，3）$的上限从$（p-1）！ - 1 $至$（p-1）到$（p-1）！ - \ lceil \ frac {p} {p} {3} {3} \ rceil+rceil+2 \ leq（p-1）！在特殊情况下，$ n $等于$ 6,7,11,13,14,15 $和$ 17 $，我们将上限$ p（n，3）$减少了$ 3,3,9,11,1,1 $和$ 4 $。
We study $P(n,3)$, the size of the largest subset of the set of all permutations $S_n$ with minimum Kendall $τ$-distance $3$. Using a combination of group theory and integer programming, we reduced the upper bound of $P(p,3)$ from $(p-1)!-1$ to $(p-1)!-\lceil\frac{p}{3}\rceil+2\leq (p-1)!-2$ for all primes $p\geq 11$. In special cases where $n$ is equal to $6,7,11,13,14,15$ and $17$ we reduced the upper bound of $P(n,3)$ by $3,3,9,11,1,1$ and $4$, respectively.
