论文标题
部分可观测时空混沌系统的无模型预测
A logical limit law for $231$-avoiding permutations
论文作者
论文摘要
我们证明，避免231级的排列能够满足逻辑上限定律，即，对于任何一阶句子$ψ$，用两个总订单的语言，概率$ p_ {n，ψ} $，是均匀的随机231个随机231-避免231个避免的尺寸$ n $ n $ n $ n $ nimips $ψ$ aft limit as a in $ n $ n $ n $ n $ n lim n $ n $。此外，我们建立了有关$ p_ {n，ψ} $的行为和价值的进一步结果：（i）它要么远离$ 0 $，要么是快速衰减； （ii）一组可能的限制在$ [0,1] $中密集。我们的工具主要来自分析组合和奇异性分析。
We prove that the class of 231-avoiding permutations satisfies a logical limit law, i.e. that for any first-order sentence $Ψ$, in the language of two total orders, the probability $p_{n,Ψ}$ that a uniform random 231-avoiding permutation of size $n$ satisfies $Ψ$ admits a limit as $n$ is large. Moreover, we establish two further results about the behavior and value of $p_{n,Ψ}$: (i) it is either bounded away from $0$, or decays exponentially fast; (ii) the set of possible limits is dense in $[0,1]$. Our tools come mainly from analytic combinatorics and singularity analysis.
