In a recent work, a central limit theorem for pattern counts in random planar maps was proven by reducing the problem to a face count problem. We provide a shorter proof by circumventing this reduction through the computation of bivariate coefficient asymptotics from a functional equation with one catalytic variable and extend the result to pattern counts with arbitrary boundary and new map classes.

翻译：在近期工作中，通过将问题简化为面计数问题，证明了随机平面地图中模式计数的一个中心极限定理。我们通过绕过这一简化、直接从带有一个催化变量的函数方程中计算双变量系数渐近性，给出了一个更短证明，并将结果推广到具有任意边界的模式计数及新的地图类别。