LargestShiftedPart

The largest part after adding i - 1 to the i-th part.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000384via IntegerPartition✓↗

LargestShiftedPart(partition)The largest part after adding i - 1 to the i-th part.

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.
• One less than MaximalRectangleHalfPerimeter, except that both are 0 on the empty partition.

Definition

Epsil, as the implementation runs it.

on IntegerPartition, over _x

0 if Length(_x) < 1 else Max(Map(
                                  Function(_x[i] + (i - 1), i),
                                  Range(1, Length(_x)),
                                ))

Examples

Basic #

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

live ↗

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

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

live ↗

In$\mathrm{LargestShiftedPart}({\operatorname{IntegerPartition}}([3, 3, 1]))$Out$4$

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St000384

FindStat's value for [2]

live ↗

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

Known value · FindStat St000384

FindStat's value for [3]

live ↗

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

Known value · FindStat St000384

About

Examples	5
Crosswalk	FindStat