A Length Function for Weyl Groups of extended affine root systems of   Type $A_1$
  In this work, we study the concept of the length function and some of its combinatorial properties for the class of extended affine root systems of type $A_1$. We introduce a notion of root basis for these root systems, and using a unique expression of the elements of the Weyl group with respect to a set of generators for the Weyl group, we calculate the length function with respect to a very specific root basis. 
Saeid Azam, Mohammad Nikouei
math.QA math.CO