CenterSize

The length of the longest subsequence a(1), ..., a(k) with a(i) <= i.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001937via ParkingFunction✓↗

CenterSize(parkingFunction)The length of the longest subsequence a(1), ..., a(k) with a(i) <= i.

Typed signatures

Type	Package	Applies
(parking_function) -> number	combinatorics	always

Domain: Parking function statistics

Details

• Defined over ParkingFunction as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a ParkingFunction 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.
• FindStat's St001937. Taking each entry that fits the next index is the longest such subsequence.

Definition

Epsil, as the implementation runs it.

on ParkingFunction, over _x

0 if Length(_x) < 1 else Fold(
                               Function(a + (1 if b <= a + 1 else 0), a, b),
                               0,
                               _x,
                             )

Examples

Basic #

the parking function $[2,1,1,4,2]$

live ↗

In$\mathrm{CenterSize}({\operatorname{ParkingFunction}}([2, 1, 1, 4, 2]))$Out$3$

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St001937

FindStat's value for [1,1]

live ↗

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

Known value · FindStat St001937

FindStat's value for [1,2]

live ↗

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

Known value · FindStat St001937

About

Examples	4
Crosswalk	FindStat