arXiv subjects
Publications and source records attributed to Akram Yousofzadeh.
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and related topics, including amenability, paradoxical decomposition and the group theoretical properties.
The Tarski number of a group $G$ is the minimal number of the pieces of paradoxical decompositions of that group. Using configurations along with a matrix combinatorial property we construct paradoxical decompositions. We also compute an upper bound for the Tarski number of a given non-amenable group by counting the number of paths in a diagram associated to the group.