Hook graph of a partition

The hook graph is the Young diagram with the hook length written in each box. It displays the hook product and thus the hook-length formula for the corresponding Specht module. This use of the name is recorded in Frame, Robinson and Thrall's original hook-graph paper; it refers to a labeled array, not a directed hook-walk graph.

The product of all hook lengths in a Young diagram is the denominator in the hook-length formula, and the scalar in the quasi-idempotence identity for its Young symmetrizer.