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, and D4, ofâ€¦ (More)

We present a polynomiality property of the Littlewood-Richardson coefficients cÎ½Î»Î¼. The coefficients are shown to be given by polynomials in Î», Î¼ and Î½ on the cones of the chamber complex of a vectorâ€¦ (More)

Parallelogram polyominoes form a subclass of convex polyominoes in the square lattice; they have been studied extensively in the literature. The enumeration of (translation-type) parallelogramâ€¦ (More)

We use Gelfandâ€“Tsetlin diagrams to write down the weight multiplicity function for the Lie algebraslkC (typeAkâˆ’1) as a single partition function. This allows us to apply known results a partitionâ€¦ (More)

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 of closed randomâ€¦ (More)

Using tools from combinatorics, convex geometry and symplectic geometry, we study the behavior of the Kostka numbers KÎ»Î² and Littlewood-Richardson coefficients cÎ»Î¼ (the typeA weight multiplicitiesâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

2004

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 weight multiplicitiesâ€¦ (More)

Parallelogram polyominoes are a subclass of convex polyominoes in the square lattice that has been studied extensively in the literature. Recently [18] congruence classes of convex polyominoes withâ€¦ (More)