Hook Length Formula

A Formula for the number of Young Tableaux associated with a given Young Diagram. Ineach box, write the sum of one plus the number of boxes horizontally to the right and vertically below the box (the ``hooklength''). The number of tableaux is then divided by the product of all ``hook lengths''. The Combinatorica`NumberOfTableaux function in Mathematica implements the hook length formula.

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.

• Aureum Theorema
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