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Standard Shifted Young Tableau


A standard shifted Young tableau is a filling of the shifted diagram of a partition lambda=(lambda_1,...,lambda_l) of n with lambda_1>...>lambda_l>0. Row i contains lambda_i boxes and starts in column i, so it is indented i-1 positions. The boxes contain each of 1, 2, ..., n exactly once, with entries increasing from left to right along rows and from top to bottom down columns (Sagan 1987, pp. 63-64).

For example, the unique standard shifted Young tableau of shape (2,1) has 1 and 2 in its first row and 3 below the 2.


See also

Partition, Young Tableau

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References

Sagan, B. E. "Shifted Tableaux, Schur Q-Functions, and a Conjecture of R. Stanley." J. Combin. Th. A 45, 62-103, 1987. https://doi.org/10.1016/0097-3165(87)90047-1.

Cite this as:

Weisstein, Eric W. "Standard Shifted Young Tableau." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StandardShiftedYoungTableau.html

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