Littlewood-Richardson coefficients as a signed sum of Kostka numbers
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 su...
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Main Author | |
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Format | Journal Article |
Language | English |
Published |
19.11.2022
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Subjects | |
Online Access | Get full text |
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Summary: | 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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DOI: | 10.48550/arxiv.2211.10669 |