Identifier
-
Mp00052:
Parking functions
—to non-decreasing parking function⟶
Parking functions
St000135: Parking functions ⟶ ℤ
Values
[1] => [1] => 1
[1,1] => [1,1] => 1
[1,2] => [1,2] => 2
[2,1] => [1,2] => 2
[1,1,1] => [1,1,1] => 1
[1,1,2] => [1,1,2] => 1
[1,2,1] => [1,1,2] => 1
[2,1,1] => [1,1,2] => 1
[1,1,3] => [1,1,3] => 2
[1,3,1] => [1,1,3] => 2
[3,1,1] => [1,1,3] => 2
[1,2,2] => [1,2,2] => 2
[2,1,2] => [1,2,2] => 2
[2,2,1] => [1,2,2] => 2
[1,2,3] => [1,2,3] => 3
[1,3,2] => [1,2,3] => 3
[2,1,3] => [1,2,3] => 3
[2,3,1] => [1,2,3] => 3
[3,1,2] => [1,2,3] => 3
[3,2,1] => [1,2,3] => 3
[1,1,1,1] => [1,1,1,1] => 1
[1,1,1,2] => [1,1,1,2] => 1
[1,1,2,1] => [1,1,1,2] => 1
[1,2,1,1] => [1,1,1,2] => 1
[2,1,1,1] => [1,1,1,2] => 1
[1,1,1,3] => [1,1,1,3] => 1
[1,1,3,1] => [1,1,1,3] => 1
[1,3,1,1] => [1,1,1,3] => 1
[3,1,1,1] => [1,1,1,3] => 1
[1,1,1,4] => [1,1,1,4] => 2
[1,1,4,1] => [1,1,1,4] => 2
[1,4,1,1] => [1,1,1,4] => 2
[4,1,1,1] => [1,1,1,4] => 2
[1,1,2,2] => [1,1,2,2] => 1
[1,2,1,2] => [1,1,2,2] => 1
[1,2,2,1] => [1,1,2,2] => 1
[2,1,1,2] => [1,1,2,2] => 1
[2,1,2,1] => [1,1,2,2] => 1
[2,2,1,1] => [1,1,2,2] => 1
[1,1,2,3] => [1,1,2,3] => 1
[1,1,3,2] => [1,1,2,3] => 1
[1,2,1,3] => [1,1,2,3] => 1
[1,2,3,1] => [1,1,2,3] => 1
[1,3,1,2] => [1,1,2,3] => 1
[1,3,2,1] => [1,1,2,3] => 1
[2,1,1,3] => [1,1,2,3] => 1
[2,1,3,1] => [1,1,2,3] => 1
[2,3,1,1] => [1,1,2,3] => 1
[3,1,1,2] => [1,1,2,3] => 1
[3,1,2,1] => [1,1,2,3] => 1
[3,2,1,1] => [1,1,2,3] => 1
[1,1,2,4] => [1,1,2,4] => 2
[1,1,4,2] => [1,1,2,4] => 2
[1,2,1,4] => [1,1,2,4] => 2
[1,2,4,1] => [1,1,2,4] => 2
[1,4,1,2] => [1,1,2,4] => 2
[1,4,2,1] => [1,1,2,4] => 2
[2,1,1,4] => [1,1,2,4] => 2
[2,1,4,1] => [1,1,2,4] => 2
[2,4,1,1] => [1,1,2,4] => 2
[4,1,1,2] => [1,1,2,4] => 2
[4,1,2,1] => [1,1,2,4] => 2
[4,2,1,1] => [1,1,2,4] => 2
[1,1,3,3] => [1,1,3,3] => 2
[1,3,1,3] => [1,1,3,3] => 2
[1,3,3,1] => [1,1,3,3] => 2
[3,1,1,3] => [1,1,3,3] => 2
[3,1,3,1] => [1,1,3,3] => 2
[3,3,1,1] => [1,1,3,3] => 2
[1,1,3,4] => [1,1,3,4] => 3
[1,1,4,3] => [1,1,3,4] => 3
[1,3,1,4] => [1,1,3,4] => 3
[1,3,4,1] => [1,1,3,4] => 3
[1,4,1,3] => [1,1,3,4] => 3
[1,4,3,1] => [1,1,3,4] => 3
[3,1,1,4] => [1,1,3,4] => 3
[3,1,4,1] => [1,1,3,4] => 3
[3,4,1,1] => [1,1,3,4] => 3
[4,1,1,3] => [1,1,3,4] => 3
[4,1,3,1] => [1,1,3,4] => 3
[4,3,1,1] => [1,1,3,4] => 3
[1,2,2,2] => [1,2,2,2] => 2
[2,1,2,2] => [1,2,2,2] => 2
[2,2,1,2] => [1,2,2,2] => 2
[2,2,2,1] => [1,2,2,2] => 2
[1,2,2,3] => [1,2,2,3] => 2
[1,2,3,2] => [1,2,2,3] => 2
[1,3,2,2] => [1,2,2,3] => 2
[2,1,2,3] => [1,2,2,3] => 2
[2,1,3,2] => [1,2,2,3] => 2
[2,2,1,3] => [1,2,2,3] => 2
[2,2,3,1] => [1,2,2,3] => 2
[2,3,1,2] => [1,2,2,3] => 2
[2,3,2,1] => [1,2,2,3] => 2
[3,1,2,2] => [1,2,2,3] => 2
[3,2,1,2] => [1,2,2,3] => 2
[3,2,2,1] => [1,2,2,3] => 2
[1,2,2,4] => [1,2,2,4] => 3
[1,2,4,2] => [1,2,2,4] => 3
[1,4,2,2] => [1,2,2,4] => 3
[2,1,2,4] => [1,2,2,4] => 3
>>> Load all 145 entries. <<<
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Description
The number of lucky cars of the parking function.
A lucky car is a car that was able to park in its prefered spot.
The generating function,
$$ q\prod_{i=1}^{n-1} (i + (n-i+1)q) $$
was established in [1].
A lucky car is a car that was able to park in its prefered spot.
The generating function,
$$ q\prod_{i=1}^{n-1} (i + (n-i+1)q) $$
was established in [1].
Map
to non-decreasing parking function
Description
Return the non-decreasing parking function which underlies the parking function.
Sorts the parking function into an increasing sequence.
Sorts the parking function into an increasing sequence.
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