标题： 关于平面堆叠的平方冰类似物 显示英文标题

标题： On a square-ice analogue of plane partitions

摘要： 我们研究一个单参数族（$\ell=1,2,3,\ldots$）的配置，这些配置是平面分拆的平方冰类比。 使用Bratley和McKay的算法，我们进行了精确计数以研究其渐近行为，并通过蒙特卡罗模拟以及显式界限确定，其渐近行为与平面分拆类似。 我们最后进行了系列分析，并提供了渐近行为的独立估计。 显示英文摘要

摘要： We study a one-parameter family ($\ell=1,2,3,\ldots$) of configurations that are square-ice analogues of plane partitions. Using an algorithm due to Bratley and McKay, we carry out exact enumerations in order to study their asymptotic behaviour and establish, via Monte Carlo simulations as well as explicit bounds, that the asymptotic behaviour is similar to that of plane partitions. We finally carry out a series analysis and provide independent estimates for the asymptotic behaviour.