an elementary method for computing the kostka coefficients

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...

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]...

On the complexity of computing Kostka numbers and Littlewood-Richardson coefficients

Kostka numbers and Littlewood-Richardson coefficients appear in combinatorics and representation theory. Interest in their computation stems from the fact that they are present in quantum mechanical computations since Wigner [15]. In recent times, there have been a number of algorithms proposed to perform this task [1–3, 11, 12]. The issue of their computational complexity has received attentio...

Explicit Plethystic Formulas for Macdonald q,t-Kostka Coefficients

i=1 ti−1 (1+· · ·+qμi−1). In [8] Garsia-Tesler proved that if γ is a partition of k and λ = (n−k, γ) is a partition of n, then there is a unique symmetric polynomial kγ(x; q, t) of degree ≤ k with the property that K̃λμ(q, t) = kγ [Bμ(q, t); q, t] holds true for all partitions μ. It was shown there that these polynomials have Schur function expansions of the form kγ(x; q, t) = ∑ |ρ|≤|γ| Sλ(x) kρ...

An Elementary Method for Tablet

This paper proposes the creation of a method book for tabletbased instruments, evaluating pedagogical materials for traditional instruments as well as research in human-computer interaction and tablet interfaces.