Littlewood-Richardson coefficients as a signed sum of Kostka numbers

2022/11/19 by Sagar Shrivastava, Shrivastava, Sagar
Mathematics · #Advanced Mathematical Identities #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2211.10669

Abstract

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.

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