SumOfHookLengths

The total of all hook lengths.

WikipediaHook length formulaMathWorldHookLengthFormulaWikidataQ17163411FindStatSt000869via IntegerPartition✓

SumOfHookLengths(partition)

Domain: Partition statistics

Details

Defined over `IntegerPartition` as an expression in `_x`, evaluated by compute-engine — the definition IS the implementation.
Takes a `IntegerPartition` and nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer.
Hook of cell (i, j) is arm + leg + 1 = (λ_i - j) + (λ'_j - i) + 1.

Examples