We study the functions that count matrices of given rank over a finite field with specified positions equal to zero. We show that these matrices are q-analogues of permutations with certainâ€¦ (More)

The algebra of symmetric functions, the representation theory of the symmetric group, and the geometry of the Grassmannian are related to each other via Schur functions, Specht modules, and Schubertâ€¦ (More)

It is well known that the set of possible degree sequences for a simple graph on n vertices is the intersection of a lattice and a convex polytope. We show that the set of possible degree sequencesâ€¦ (More)

We introduce a Littlewood-Richardson rule based on an algorithmic deformation of skew Young diagrams and present a bijection with the classical rule. The result is a direct combinatorialâ€¦ (More)

The Fominâ€“Kirillov algebra En is a noncommutative algebra with a generator for each edge of the complete graph on n vertices. For any graph G on n vertices, let EG be the subalgebra of En generatedâ€¦ (More)

We introduce a Littlewood-Richardson rule based on an algorithmic deformation of skew Young diagrams and present a bijection with the classical rule. The result is a direct combinatorialâ€¦ (More)