2011/12/30 by Cannon, J. W., Floyd, W. J., Parry, W. R.
#20F65 (Secondary) #43A07 (Primary) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1201.0132
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.