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TU Berlin

Inhalt des Dokuments

Ehemalige Mitarbeiter

Dr. Christian Ikenmeyer

Lupe

Kontakt
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

Deciding Positivity of Littlewood-Richardson coefficients
Zitatschlüssel BI-Deciding-Positivity-Of-Littlewood-Richardson-Coefficients
Autor Peter Bürgisser and Christian Ikenmeyer
Seiten 1639-1681
Jahr 2013
DOI 10.1137/120892532
Journal SIAM J. Discrete Math.
Jahrgang 27
Nummer 4
Notiz Java-Applet: http://www3.math.tu-berlin.de/algebra/flowapplet/
Zusammenfassung 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.
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