13 citations · 24 across the 6 of their papers we have counts for
6 papers
Signature quantization, representations of compact Lie groups, and a q-analogue of the Kostant partition function
Victor Guillemin, Etienne Rassart
We discuss some applications of signature quantization to the representation theory of compact Lie groups. In particular, we prove signature analogues of the Kostant formula for we…
A polynomiality property for Littlewood-Richardson coefficients
Etienne Rassart
We present a polynomiality property of the Littlewood-Richardson coefficients c_{λμ}^ν. The coefficients are shown to be given by polynomials in λ, μand νon the cones of the chambe…
Path counting and random matrix theory
Ioana Dumitriu, Etienne Rassart
We establish three identities involving Dyck paths and alternating Motzkin paths, whose proofs are based on variants of the same bijection. We interpret these identities in terms o…
A vector partition function for the multiplicities of sl_k(C)
Sara Billey, Victor Guillemin, Etienne Rassart
We use Gelfand-Tsetlin diagrams to write down the weight multiplicity function for the Lie algebra sl_k(C) (type A_{k-1}) as a single partition function. This allows us to apply kn…
Enumeration of Symmetry Classes of Parallelogram Polyominoes
Pierre Leroux, Etienne Rassart
Parallelogram polyominoes are a subclass of convex polyominoes in the square lattice that has been studied extensively in the literature. Recently congruence classes of convex poly…
Enumeration of symmetry classes of convex polyominoes in the square lattice
Pierre Leroux, Etienne Rassart, Ariane Robitaille
This paper concerns the enumeration of rotation-type and congruence-type convex polyominoes on the square lattice. These can be defined as orbits of the groups C4, of rotations, an…