  Littlewood-Richardson (LR) coefficients and Kostka Numbers appear in
representation theory and combinatorics related to $GL_n$. It is known that
Kostka numbers can be represented as special Littlewood-Rischardson
coefficient. In this paper, we show how one can represent LR coefficient as a
signed sum of Kostka numbers, and use the formulation to give a polynomial time
algorithm for the same, hence showing that they belong to the same class of
decision problems. As a corollary, we will prove Steinberg's formula using
Kostant's partition function.
