HookProduct
The product of all hook lengths — the denominator in the hook-length formula.
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Hook length formulaMathWorldHookLengthFormulaWikidataQ17163411FindStatSt000179via IntegerPartition✓HookProduct(partition)The product of all hook lengths — the denominator in the hook-length formula.Typed signatures
| Type | Package | Applies |
|---|---|---|
(integer_partition) -> number | combinatorics | always |
Details
- Defined over
IntegerPartitionas an expression in_x, evaluated by compute-engine — the definition IS the implementation. - Takes a
IntegerPartitionand 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.
Definition
Epsil, as the implementation runs it.
on IntegerPartition, over _x
1 if Length(_x) < 1 else Product(Map(Function(Product(Map(
Function(_x[i] - j +
(Map(
Function(Count(Filter(
Range(1, Length(_x)),
Function(_x[j] >= i, j),
)), i),
Range(1, Max(_x)),
)[j] - i) + 1, j),
Range(1, _x[i]),
)), i), Range(
1,
Length(_x),
)))