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Skew Tableau


A skew tableau is a filling of the boxes remaining when the Ferrers diagram of a partition mu is removed from that of a partition lambda containing it. Its shape is denoted lambda/mu. A semistandard skew tableau has positive integer entries weakly increasing along rows and strictly increasing down columns. Its content records how often each entry occurs. A standard skew tableau uses each of 1, 2, ..., |lambda|-|mu| exactly once, with entries strictly increasing along rows and down columns. The empty inner partition gives an ordinary Young tableau (Macdonald 1995).

Littlewood-Richardson coefficients count certain semistandard skew tableaux with a lattice-word condition.


See also

Ferrers Diagram, Littlewood-Richardson Coefficient, Young Tableau

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References

Macdonald, I. G. Symmetric Functions and Hall Polynomials, 2nd ed. Oxford, England: Oxford University Press, 1995.

Cite this as:

Weisstein, Eric W. "Skew Tableau." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SkewTableau.html

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