In this paper, we first establish a version of the central limit theorem for a double sequence $\{p_i(n)\}$ that satisfies a linear recurrence relation. Then we find and prove that under some commonly observed conditions, the sequence of embedding distributions of an H-linear family of graphs with spiders is asymptotic to a normal distribution. Applications are given to some well-known path-like and ring-like sequences of graphs. We also prove that the limit for the Euler-genus distributions of a sequence of graphs is the same as the limit for the crosscap-number distributions of that sequence.

中文翻译：

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嵌入分布的限制

在本文中，我们首先为双序列建立中心极限定理的一个版本 $\{p_{\mathrm{一世}}（ñ）\}$满足线性递归关系。然后我们发现并证明，在一些通常观察到的条件下，带有蜘蛛的H线性图族的嵌入分布序列渐近于正态分布。给出了一些众所周知的图的类路径和类环序列的应用。我们还证明了图序列的Euler-属分布的极限与该序列的交叉帽数分布的极限相同。