Degrees of stretched Kostka coefficients

Degrees of Stretched Kostka Coefficients

Given a partition λ and a composition β, the stretched Kostka coefficient Kλβ(n) is the map n 7→ Knλ,nβ sending each positive integer n to the Kostka coefficient indexed by nλ and nβ. Derksen and Weyman [DW02] have shown that stretched Kostka coefficients are polynomial functions of n. King, Tollu, and Toumazet have conjectured that these polynomials always have nonnegative coefficients [KTT04]...

RIMS - 1824 Rigged Configurations and Catalan , Stretched Parabolic Kostka

We will look at the Catalan numbers from the Rigged Configurations point of view originated [9] from an combinatorial analysis of the Bethe Ansatz Equations associated with the higher spin anisotropic Heisenberg models . Our strategy is to take a combinatorial interpretation of Catalan numbers Cn as the number of standard Young tableaux of rectangular shape (n2), or equivalently, as the Kostka ...

Generalised stretched Littlewood-Richardson coefficients

In this paper we investigate Q(n) = Q λ′,μ′ (n) = P ν c(nλ + λ;nμ+ μ, ν) as a function of n and show that Q(n) is bounded above if and only if λ/μ is a partition or rotated partition. Here c(λ;μ, ν) is the LittlewoodRichardson coefficient. So Q(n) counts the number of LR tableaux of shape (nλ + λ)/(nμ + μ) or the total number of irreducible characters in the skew character [(nλ+ λ)/(nμ + μ)]. W...

An Elementary Method for Computing the Kostka Coefficients

Geometric approaches to computing Kostka numbers and Littlewood-Richardson coefficients

Using tools from combinatorics, convex geometry and symplectic geometry, we study the behavior of the Kostka numbers Kλβ and Littlewood-Richardson coefficients cλμ (the type A weight multiplicities and Clebsch-Gordan coefficients). We show that both are given by piecewise polynomial functions in the entries of the partitions and compositions parametrizing them, and that the domains of polynomia...