@inproceedings{BI-A-Max-Flow-Algorithm-For-Positivity-Of-Littlewood-Richardson-Coefficients,
Title = {A max-flow algorithm for positivity of Littlewood-Richardson coefficients},
Author = {Peter Bürgisser and Christian Ikenmeyer},
Booktitle = {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 $\mathrm{GL}(n,\mathbb C)$. 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},
Url = {http://www3.math.tu-berlin.de/algebra/work/maxflow.pdf},
Reviewed = {True}
}