在单调模式（大部分）规则的地方
Where the monotone pattern (mostly) rules
摘要：
我们用一个非常严格的定义来考虑模式包含和避免，这个定义是Riordan在60多年前首先使用的。使用这个定义，我们证明了单调模式是更容易避免比几乎任何其他模式的相同长度。我们还表明，与此定义，几乎所有的模式的长度$k$避免了相同数量的排列长度$n$。对于模式包含的更宽松的定义，相应的陈述并不为真。这是我们第一次知道期望值被用来比较避免某些模式的排列数。
英文摘要：
We consider pattern containment and avoidance with a very tight definition that was used first by Riordan more than 60 years ago. Using this definition, we prove the monotone pattern is easier to avoid than almost any other pattern of the same length. We also show that with this definition, almost all patterns of length $k$ are avoided by the same number of permutations of length $n$. The corresponding statements are not known to be true for more relaxed definitions of pattern containment. This is the first time we know of that expectations are used to compare numbers of permutations avoiding certain patterns.
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