Generalised Stretched Littlewood-Richardson Coefficients

Details Generalised Stretched Littlewood-Richardson Coefficients Generalised Stretched Littlewood-Richardson Coefficients

2009-04-30

arxiv.org/abs/0904.4778v3

J. Combin. Theory Ser. A 118 (2011) 1829-1842

Mathematics

Combinatorics

15 pages, rewritten with more results and examples (compared with v1), final version to appear at Journal of Combinatorial The

Scientific paper

10.1016/j.jcta.2011.02.005

The Littlewood-Richardson (LR) coefficient counts among many other things the LR tableaux of a given shape and a given content. We prove, that the number of LR tableaux weakly increases if one adds to the shape and the content the shape and the content of another LR tableau. We also investigate the behaviour of the number of LR tableaux, if one repeatedly adds to the shape another shape with either fixed or arbitrary content. This is a generalisation of the stretched LR coefficients, where one repeatedly adds the same shape and content to itself.

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