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Hook Length Formula


A formula for the number of Young tableaux associated with a given Ferrers diagram. In each box, write the sum of one plus the number of boxes horizontally to the right and vertically below the box (the "hook length"). The number of tableaux is then n! divided by the product of all "hook lengths."


See also

Ferrers Diagram, Young Tableau

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References

Jones, V. "Hecke Algebra Representations of Braid Groups and Link Polynomials." Ann. Math. 126, 335-388, 1987.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.

Referenced on Wolfram|Alpha

Hook Length Formula

Cite this as:

Weisstein, Eric W. "Hook Length Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HookLengthFormula.html

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