论文标题
某些网格模式的围困的渐近行为
Asymptotic Behaviour of the Containment of Certain Mesh Patterns
论文作者
论文摘要
我们在长度$ n $的排列比例中介绍了一些结果，其中包含某些网格模式，因为$ n $增长了，并在某些情况下给出了精确的枚举结果。特别是，我们专注于整个行和列的阴影的网格模式。我们证明了一些适用于任何长度的网格模式的一般结果，然后考虑长度四的网格模式。这些结果的重要结果是表明，包含网格模式的排列比例可以在$ 0 $和$ 1 $之间的范围范围较高的值。
We present some results on the proportion of permutations of length $n$ containing certain mesh patterns as $n$ grows large, and give exact enumeration results in some cases. In particular, we focus on mesh patterns where entire rows and columns are shaded. We prove some general results which apply to mesh patterns of any length, and then consider mesh patterns of length four. An important consequence of these results is to show that the proportion of permutations containing a mesh pattern can take a wide range of values between $0$ and $1$.
