LuckyCars

The cars that park in the spot they prefer.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000135via ParkingFunction✓↗

LuckyCars(parkingFunction)The cars that park in the spot they prefer.

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 St000135.

Definition

Epsil, as the implementation runs it.

on ParkingFunction, over _x

0 if Length(_x) < 1 else Max(Sum(Map(Function(1 if (1 if Max(Map(
                                                                  Function(Max(Sum(Map(
                                                                                        Function(1 if j <=
                                                                                                      i - 1 &&
                                                                                                      _x[j] >= a &&
                                                                                                      _x[j] <= _x[i] else 0, j),
                                                                                        Range(1, Length(_x)),
                                                                                      )), 0) -
                                                                           (_x[i] +
                                                                            1 - a), a),
                                                                  Range(
                                                                         1,
                                                                         _x[i],
                                                                       ),
                                                                )) >= 0 else 0) ==
                                                   0 else 0, i), Range(
                                                                       1,
                                                                       Length(_x),
                                                                     ))), 0)

Examples

Basic #

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

live ↗

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

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St000135

FindStat's value for [1,1]

live ↗

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

Known value · FindStat St000135

FindStat's value for [1,2]

live ↗

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

Known value · FindStat St000135

About

Examples	4
Crosswalk	FindStat