We study the class $\mathcal C$ of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape. Included in this class are the Hall-Littlewood polynomials, $k$-Schur functions, and Stanley symmetric functions; functions whose Schur coefficients encode combinatorial, representation theoretic and geometric information. While Schur functions represent the cohomology of the Grassmannian variety of $GL_n$, Grothendieck functions $\{G_\lambda\}$ represent the $K$-theory of the same space. In this paper, we give a combinatorial description of the coefficients when any element of $\mathcal C$ is expanded in the $G$-basis or the basis dual to $\{G_\lambda\}$.
@article{10_37236_2320,
author = {Jason Bandlow and Jennifer Morse},
title = {Combinatorial expansions in {\(K\)-theoretic} bases},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {4},
doi = {10.37236/2320},
zbl = {1267.05037},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2320/}
}
TY - JOUR
AU - Jason Bandlow
AU - Jennifer Morse
TI - Combinatorial expansions in \(K\)-theoretic bases
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/2320/
DO - 10.37236/2320
ID - 10_37236_2320
ER -
%0 Journal Article
%A Jason Bandlow
%A Jennifer Morse
%T Combinatorial expansions in \(K\)-theoretic bases
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/2320/
%R 10.37236/2320
%F 10_37236_2320
Jason Bandlow; Jennifer Morse. Combinatorial expansions in \(K\)-theoretic bases. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2320
