Deciding Positivity of Littlewood-Richardson Coefficients [article]

Peter Bürgisser, Christian Ikenmeyer
2013 arXiv   pre-print
Starting with Knutson and Tao's hive model (in J. Amer. Math. Soc., 1999) we characterize the Littlewood-Richardson coefficient c_λ,μ^ν of given partitions λ,μ,ν∈ 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_λ,μ^ν >0. This algorithm is easy to state and takes O(n^3 ν_1) arithmetic operations and comparisons. We further show that the capacity achieving hive flows can be seen as the vertices of a
more » ... ected graph, which leads to new structural insights into Littlewood-Richardson coefficients.
arXiv:1204.2484v2 fatcat:erpm3pswvfckhjotm5kgd7ukuy