CellsOutsideFirstHook

Cells in neither the first row nor the first column: the size minus the hook length of cell (1,1).

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001175via IntegerPartition✓↗

CellsOutsideFirstHook(partition)Cells in neither the first row nor the first column: the size minus the hook length of cell (1,1).

Typed signatures

Type	Package	Applies
(integer_partition) -> number	combinatorics	always

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.

Definition

Epsil, as the implementation runs it.

on IntegerPartition, over _x

0 if Length(_x) < 1 else Sum(_x) - (Max(_x) + Length(_x) - 1)

Examples

Basic #

the partition $4 + 2 + 1$ of $7$

live ↗

In$\mathrm{CellsOutsideFirstHook}({\operatorname{IntegerPartition}}([4, 2, 1]))$Out$1$

the partition $3 + 3 + 1$ of $7$

live ↗

In$\mathrm{CellsOutsideFirstHook}({\operatorname{IntegerPartition}}([3, 3, 1]))$Out$2$

Properties #

FindStat's value for [1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([1]), \text{CellsOutsideFirstHook})$Out$0$

Known value · FindStat St001175

FindStat's value for [2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([2]), \text{CellsOutsideFirstHook})$Out$0$

Known value · FindStat St001175

FindStat's value for [3]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([3]), \text{CellsOutsideFirstHook})$Out$0$

Known value · FindStat St001175

About

Examples	5
Crosswalk	FindStat