Abstract: Let G be a countable group. A mutliorder is a collection of 
bijections from G to Z (the integers) on which G acts by a special 
"double shift". If G is amenable, we also require some uniform Folner 
property of the order intervals. The main thing is that mutiorder exists 
on every countable amenable group, which can be proved using tilings.
For now, multiorder provides an alternative formula for entropy of a 
process and we are sure in the nearest future it will allow at produce 
an effective formula for the Pinsker sigma-algebra. And we hope for 
many more applications. 


This is work in progress with Piotr Oprocha (Kraków) and Guohua 
Zhang (Shanghai).