论文标题
Littlewood-Richardson系数作为Kostka数字的签名总和
Littlewood-Richardson coefficients as a signed sum of Kostka numbers
论文作者
论文摘要
Littlewood-Richardson（LR）系数和Kostka数字出现在表示理论和与$ GL_N $有关的组合中。众所周知，Kostka数字可以表示为特殊的Littlewood-Rischardson系数。在本文中，我们展示了如何将LR系数表示为Kostka数字的签名总和，并使用该公式给出了相同的多项式时间算法，因此表明它们属于同一类决策问题。作为推论，我们将使用Kostant的分区功能证明Steinberg的公式。
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.
