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Refereed Contributions

A max-flow algorithm for positivity of Littlewood-Richardson coefficients
Citation key BI-A-Max-Flow-Algorithm-For-Positivity-Of-Littlewood-Richardson-Coefficients
Author Peter Bürgisser and Christian Ikenmeyer
Title of Book FPSAC 2009
Pages 267-278
Year 2009
Address Hagenberg, Austria
Series DMTCS proc. AK
Abstract Littlewood-Richardson coefficients are the multiplicities in the tensor product decomposition of two irreducible representations of the general linear group $\mathrmGL(n,\mathbb C)$. They have a wide variety of interpretations in combinatorics, representation theory and geometry. Mulmuley and Sohoni pointed out that it is possible to decide the positivity of Littlewood-Richardson coefficients in polynomial time. This follows by combining the saturation property of Littlewood-Richardson coefficients (shown by Knutson and Tao 1999) with the well-known fact that linear optimization is solvable in polynomial time. We design an explicit combinatorial polynomial time algorithm for deciding the positivity of Littlewood-Richardson coefficients. This algorithm is highly adapted to the problem and it is based on ideas from the theory of optimizing flows in networks
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