论文标题
有限的仿射排列II。避免减少模式
Bounded affine permutations II. Avoidance of decreasing patterns
论文作者
论文摘要
我们继续研究仿生置换的新界限条件，这是由统计物理学周期性边界条件的富有成果的概念所激发的。我们专注于尺寸$ n $的有限仿射排列，避免单调降低固定尺寸$ m $的模式。我们证明，此类排列的数量渐近地等于$（M-1）^{2n} n^{（M-2）/2} $ timess显式常数为$ n \ to \ infty $。例如，避免$ 321 $的大小$ n $的有限仿射排列的数量在渐近上等于$ 4^n（n/4π）^{1/2} $。我们还证明了此类随机排列的缩放限制的缩放限制，这表明典型的有界仿射排列避免了$ m \ cdots1 $的绘图，看起来像$ M-1 $ slope $ 1 $的随机线，其$ y $ y $ y $ intercepts sum sum sugs总和$ 0 $ $ 0 $。
We continue our study of a new boundedness condition for affine permutations, motivated by the fruitful concept of periodic boundary conditions in statistical physics. We focus on bounded affine permutations of size $N$ that avoid the monotone decreasing pattern of fixed size $m$. We prove that the number of such permutations is asymptotically equal to $(m-1)^{2N} N^{(m-2)/2}$ times an explicit constant as $N\to\infty$. For instance, the number of bounded affine permutations of size $N$ that avoid $321$ is asymptotically equal to $4^N (N/4π)^{1/2}$. We also prove a permuton-like result for the scaling limit of random permutations from this class, showing that the plot of a typical bounded affine permutation avoiding $m\cdots1$ looks like $m-1$ random lines of slope $1$ whose $y$ intercepts sum to $0$.
