@article{BI-Deciding-Positivity-Of-Littlewood-Richardson-Coefficients,
Title = {Deciding Positivity of Littlewood-Richardson coefficients},
Author = {Peter Bürgisser and Christian Ikenmeyer},
Pages = {1639-1681},
Year = {2013},
Doi = {10.1137/120892532},
Journal = {SIAM J. Discrete Math.},
Volume = {27},
Number = {4},
Note = {Java-Applet: http://www3.math.tu-berlin.de/algebra/flowapplet/},
Abstract = {Starting with Knutson and Tao's hive model (in J. Amer. Math. Soc., 1999) we characterize the Littlewood-Richardson coefficient $c_{\lambda,\mu}^\nu$ of given partitions $\lambda,\mu,\nu\in\mathbb N^n$ as the number of capacity achieving hive flows on the honeycomb graph. Based on this, we design a polynomial time algorithm for deciding $c_{\lambda,\mu}^\nu >0$. This algorithm is easy to state and takes $O(n^3 \log \nu_1)$ arithmetic operations and comparisons. We further show that the capacity achieving hive flows can be seen as the vertices of a connected graph, which leads to new structural insights into Littlewood-Richardson coefficients.},
Url = {http://www3.math.tu-berlin.de/algebra/work/LRC-decide.pdf},
Url2 = {http://dx.doi.org/10.1137/120892532}
}