Presentation
A max-flow algorithm for positivity of Littlewood-Richardson coefficients
Author/s | Bürgisser, Peter
Ikenmeyer, Christian |
Publication Date | 2009-11 |
Deposit Date | 2016-02-22 |
Published in |
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Abstract | Littlewood-Richardson coefficients appear as limits of certain families of Kronecker coefficients. They have a wide variety of interpretations in combinatorics, representation theory and geometry. Mulmuley and Sohoni pointed ... Littlewood-Richardson coefficients appear as limits of certain families of Kronecker coefficients. 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. |
Citation | Bürgisser, P. y Ikenmeyer, C. (2009). A max-flow algorithm for positivity of Littlewood-Richardson coefficients. |
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