MaximalRectangleHalfPerimeter

Half the perimeter of the rectangle inside the diagram that has the greatest perimeter.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000380via IntegerPartition✓↗

MaximalRectangleHalfPerimeter(partition)Half the perimeter of the rectangle inside the diagram that has the greatest perimeter.

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 more than LargestShiftedPart, 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, i), Range(1, Length(_x))))

Examples

Basic #

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

live ↗

In$\mathrm{MaximalRectangleHalfPerimeter}({\operatorname{IntegerPartition}}([4, 2, 1]))$Out$5$

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

live ↗

In$\mathrm{MaximalRectangleHalfPerimeter}({\operatorname{IntegerPartition}}([3, 3, 1]))$Out$5$

Properties #

FindStat's value for [1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([1]), \text{MaximalRectangleHalfPerimeter})$Out$2$

Known value · FindStat St000380

FindStat's value for [2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([2]), \text{MaximalRectangleHalfPerimeter})$Out$3$

Known value · FindStat St000380

FindStat's value for [3]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([3]), \text{MaximalRectangleHalfPerimeter})$Out$4$

Known value · FindStat St000380

About

Examples	5
Crosswalk	FindStat