A simple definition for the universal Grassmannian order

In this paper, we provide a combinatorial definition of the Universal Grassmannian order (or the Grassmannian Bruhat order) of Bergeron and Sottile. This defines the order in terms of inversions, and thus the order can be viewed as a generalization of the weak order for Coxeter groups. Finally, we use this understanding of the order to analyze the generating function of the number of elements at rank n in this order.