In this paper, we demonstrate a method for calculating the production matrices for the Euler-genus polynomials of H-linear families of graphs. Particularly, for any ladder-like sequence of graphs, we give its explicit production matrix that leads to a recurrence relation. Based on this recurrence relation, we show that the Euler-genus distributions of any ladder-like sequence of graphs are asymptotic to a normal distribution. Since the genus polynomials of the ladder-like sequence of graphs have already been calculated by Chen et al.(J Algebr Combin 52:137–155, 2020), their crosscap-number polynomials are also known.

中文翻译：

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图的梯形图序列的Euler-属分布的极限

在本文中，我们演示了一种计算H线性图族的Euler属多项式的乘积矩阵的方法。特别是，对于任何类似梯形图的序列，我们给出其明确的产生矩阵，从而导致递归关系。基于这种递归关系，我们表明图的任何梯形序列的欧拉属分布都正态分布。由于Chen等人已经计算了梯形图序列的属多项式（J Algebr Combin 52：137–155，2020），因此它们的跨帽数多项式也是已知的。