Factorisation of Littlewood-Richardson coefficients
King, Ronald C., Tollu, Christophe and Toumazet, Frederic (2009) Factorisation of Littlewood-Richardson coefficients. Journal of Combinatorial Theory, Series A, 116, (2), 314-333. (doi:10.1016/j.jcta.2008.06.005)
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Official URL: http://dx.doi.org/10.1016/j.jcta.2008.06.005
Description/Abstract
The hive model is used to show that the saturation of any essential Horn inequality leads to the factorisation of Littlewood-Richardson coefficients. The proof is based on the use of combinatorial objects known as puzzles. These are shown not only to account for the origin of Horn inequalities, but also to determine the constraints on hives that lead to factorisation. Defining a primitive Littlewood-Richardson coefficient to be one for which all essential Horn inequalities are strict, it is shown that every Littlewood-Richardson coefficient can be expressed as a product of primitive coefficients. Precisely the same result is shown to apply to the polynomials defined by stretched Littlewood-Richardson coefficients.
| Item Type: | Article |
|---|---|
| ISSN: | 0097-3165 (print) |
| Uncontrolled Keywords: | littlewood-richardson coefficients, hive model, horn inequalities, puzzles, factorisation, lr-polynomials |
| Related URLs: | http://dx.doi.org/10.1016/j.jc...008.06.005 |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics |
| ePrint ID: | 66211 |
| Deposited On: | 12 Jan 2010 |
| Last Modified: | 01 Sep 2011 14:02 |
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