标题： 可迁性，富诺集，冷却函数 显示英文标题

标题： Amenability, Folner sets, and cooling functions

摘要： 埃尔林·福勒证明了一个可数群的可迁性或非可迁性取决于其有限子集的复杂性。复杂性有三个度量标准：最大福勒比值、最优冷却函数和最小冷却范数。我们的第一个目标是展示对于固定的有限子集，这三个度量标准紧密相关。然后我们探讨它们的算法计算方法。我们的意图是为通过算法探索离散群的可迁性和非可迁性提供理论基础。 显示英文摘要

摘要： Erling Folner proved that the amenability or nonamenability of a countable group depends on the complexity of its finite subsets. Complexity has three measures: maximum Folner ratio, optimal cooling function, and minimum cooling norm. Our first aim is to show that, for a fixed finite subset, these three measures are tightly bound to one another. We then explore their algorithmic calculation. Our intent is to provide a theoretical background for algorithmically exploring the amenability and nonamenability of discrete groups.