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Dr. Christian Ikenmeyer
- © Christian Ikenmeyer
University of Liverpool
Department of Computer Science
Ashton Building, Office 311
Ashton Street, Liverpool, L69 3BX
United Kingdom Persönliche Homepage
http://pcwww.liv.ac.uk/~iken/
Publikationen in der Arbeitsgruppe
| Citation key | BI-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 $c_łambda,\mu^\nu$ of given partitions $łambda,\mu,\nu\in\mathbb N^n$ as the number of capacity achieving hive flows on the honeycomb graph. Based on this, we design a polynomial time algorithm for deciding $c_łambda,\mu^\nu >0$. This algorithm is easy to state and takes $O(n^3 łog \nu_1)$ 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. |