论文标题
计算圆柱体上的国王排列
Counting King Permutations on the Cylinder
论文作者
论文摘要
如果每种$ | |σ_i-σ__{i+1} {i+1} |> 1 $ 1 \ leq I \ leq i \ leq i \ leq n-1 $ and $ | feq n-1 $ and $ | | f leq n-1 $ and $ | f leq n-1 $ and $ | f leq n-1 $ and $ | f leq n-1 $ and $ | | f leq n-1 $ and $ | | fen，我们将$σ= [σ_1，\ dots，\ dots，\ dots，= dots，σ_n] \ in s_n $ a {\ em a {\ em a我们为圆柱王排列的分布提供了一些结果，包括一些有趣的递归。我们还计算了它们在“国王排列”集中的渐近比例，即仅满足上面两个条件中的第一个。以此目的，我们定义了一个有关排列的新参数，即{\ em Cyclict键}的数量，该键是键数的修改。此外，我们还提出了有关此参数分布的一些结果。
We call a permutation $σ=[σ_1,\dots,σ_n] \in S_n$ a {\em cylindrical king permutation} if $ |σ_i-σ_{i+1}|>1$ for each $1\leq i \leq n-1$ and $|σ_1-σ_n|>1$. We present some results regarding the distribution of the cylindrical king permutations, including some interesting recursions. We also calculate their asymptotic proportion in the set of the 'king permutations', i.e. the ones which satisfy only the first of the two conditions above. With this aim we define a new parameter on permutations, namely, the number of {\em cyclic bonds} which is a modification of the number of bonds. In addition, we present some results regarding the distribution of this parameter.
