Combinatorics of diagrams of permutations

There are numerous combinatorial objects associated to a Grassmannian permutation wλ that index cells of the totally nonnegative Grassmannian. We study some of these objects (rook placements, acyclic orientations, various restricted fillings) and their q-analogues in the case of permutations w that are not necessarily Grassmannian. R´esum´e. Il y a nombreaux objets combinatoires associ´es `a une permutation Grassmannienne wλ qui indexent les cellules de le Grassmannien totalement non n´egatif. Nous ´etudions certains de ces objets (placement de tours, orientations acycliques, diverses remplissages restrentes) et leurs q-analogues dans le cas o`u la permutation w n’est pas n´ecessairement Grassmannienne.

• Type: Journal
• Year: 2016
• Where: JCT
• Authors: Joel Brewster Lewis, Alejandro H. Morales
• Keywords: JCT 2016