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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 $łambda,mu,nuinmathbb N^n$ 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.

Link zur Publikation [1] Link zur Originalpublikation [2] Download Bibtex Eintrag [3]

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[1] http://www3.math.tu-berlin.de/algebra/work/LRC-deci
de.pdf

[2] http://dx.doi.org/10.1137/120892532

[3] https://www.math.tu-berlin.de/fachgebiete_ag_diskal
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[4] https://www.math.tu-berlin.de/fachgebiete_ag_diskal
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