The set of Grassmannian permutations is described as the set of permutations having at most one descent. In this thesis, we study restrictions of pattern-avoidance and parity for these permutations. Specifically, we study the odd Grassmannian permutations that avoid patterns of size three. We derive recurrence relations and generating functions for such permutations, as well as connections to other combinatorial objects such as symmetric convex polygons, Dyck paths, and multigraphs.
