论文标题
部分可观测时空混沌系统的无模型预测
Counting crucial permutations with respect to monotone patterns
论文作者
论文摘要
最近，Avgustinovich，Kitaev和Taranenko定义了五种类型的$（k，\ ell） - $ cocucial clucial置换，这些排列不包含长度$ k $的子序列的增加或长度$ \ ell $的下降。此外，Avgustinovich，Kitaev和Taranenko开始了$（k，\ ell）的枚举 - $最小长度的关键排列和下一个最小的长度以及$（k，3） - $（$ $ $（$） - $至关重要的$（$ $（k，el）$ crucial $ crucial-crucial-crucial-crucial-crucial-crucial tense。在本文中，我们完成了Avgustinovich，Kitaev和Taranenko开始的枚举。
Recently, Avgustinovich, Kitaev, and Taranenko defined five types of $(k, \ell)-$crucial permutations, which are maximal permutations that do not contain an increasing subsequence of length $k$ or a decreasing subsequence of length $\ell$. Further, Avgustinovich, Kitaev, and Taranenko began the enumeration of the $(k, \ell)-$crucial permutations of the minimal length and the next minimal length and the $(k, 3)-$crucial permutations of all lengths for each of the five types of $(k,\ell)-$crucial permutations. In this paper, we complete the enumeration that Avgustinovich, Kitaev, and Taranenko began.
