Partitions, Kostka Polynomials and Pairs of Trees

Composition Kostka functions

Macdonald defined two-parameter Kostka functions Kλμ(q, t) where λ, μ are partitions. The main purpose of this paper is to extend his definition to include all compositions as indices. Following Macdonald, we conjecture that also these more general Kostka functions are polynomials in q and t with non-negative integers as coefficients. If q = 0 then our Kostka functions are Kazhdan-Lusztig polyn...

An Elementary Method for Computing the Kostka Coefficients

Hall-littlewood Vertex Operators and Generalized Kostka Polynomials Mark Shimozono and Mike Zabrocki

Kostka-Folkes polynomials may be considered as coefficients of the formal power series representing the character of certain graded GL(n)-modules. These GL(n)-modules are defined by twisting the coordinate ring of the nullcone by a suitable line bundle [1] and the definition may be generalized by twisting the coordinate ring of any nilpotent conjugacy closure in gl(n) by a suitable vector bundl...

Stirling number of the fourth kind and lucky partitions of a finite set

The concept of Lucky k-polynomials and in particular Lucky χ-polynomials was recently introduced. This paper introduces Stirling number of the fourth kind and Lucky partitions of a finite set in order to determine either the Lucky k- or Lucky χ-polynomial of a graph. The integer partitions influence Stirling partitions of the second kind.

Calogero-moser Space and Kostka Polynomials

We consider the canonical map from the Calogero-Moser space to symmetric powers of the affine line, sending conjugacy classes of pairs of n×n-matrices to their eigenvalues. We show that the character of a natural C∗-action on the scheme-theoretic zero fiber of this map is given by Kostka polynomials.