Hook length formula

In combinatorial mathematics, the hook length formula is a formula for the number of standard Young tableaux whose shape is a given Young diagram.It has applications in diverse areas such as representation theory, probability, and algorithm analysis; for example, the problem of longest increasing subsequences. A related formula counts the number of semi-standard Young tableaux, which is a specialization of a Schur polynomial.

Hook length formula

In combinatorial mathematics, the hook length formula is a formula for the number of standard Young tableaux whose shape is a given Young diagram.It has applications in diverse areas such as representation theory, probability, and algorithm analysis; for example, the problem of longest increasing subsequences. A related formula counts the number of semi-standard Young tableaux, which is a specialization of a Schur polynomial.