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 
divided by the product of all "hook lengths."
Hook Length Formula
See also
Ferrers Diagram, Young TableauExplore with Wolfram|Alpha
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 FormulaCite this as:
Weisstein, Eric W. "Hook Length Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HookLengthFormula.html