- FindStat

Identifier

Mp00319: Parking functions —to composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000228: Integer partitions ⟶ ℤ

Values

[1] => [1] => [1] => 1

[1,1] => [1,1] => [1,1] => 2

[1,2] => [1,2] => [2,1] => 3

[2,1] => [2,1] => [2,1] => 3

[1,1,1] => [1,1,1] => [1,1,1] => 3

[1,1,2] => [1,1,2] => [2,1,1] => 4

[1,2,1] => [1,2,1] => [2,1,1] => 4

[2,1,1] => [2,1,1] => [2,1,1] => 4

[1,1,3] => [1,1,3] => [3,1,1] => 5

[1,3,1] => [1,3,1] => [3,1,1] => 5

[3,1,1] => [3,1,1] => [3,1,1] => 5

[1,2,2] => [1,2,2] => [2,2,1] => 5

[2,1,2] => [2,1,2] => [2,2,1] => 5

[2,2,1] => [2,2,1] => [2,2,1] => 5

[1,2,3] => [1,2,3] => [3,2,1] => 6

[1,3,2] => [1,3,2] => [3,2,1] => 6

[2,1,3] => [2,1,3] => [3,2,1] => 6

[2,3,1] => [2,3,1] => [3,2,1] => 6

[3,1,2] => [3,1,2] => [3,2,1] => 6

[3,2,1] => [3,2,1] => [3,2,1] => 6

[1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 4

[1,1,1,2] => [1,1,1,2] => [2,1,1,1] => 5

[1,1,2,1] => [1,1,2,1] => [2,1,1,1] => 5

[1,2,1,1] => [1,2,1,1] => [2,1,1,1] => 5

[2,1,1,1] => [2,1,1,1] => [2,1,1,1] => 5

[1,1,1,3] => [1,1,1,3] => [3,1,1,1] => 6

[1,1,3,1] => [1,1,3,1] => [3,1,1,1] => 6

[1,3,1,1] => [1,3,1,1] => [3,1,1,1] => 6

[3,1,1,1] => [3,1,1,1] => [3,1,1,1] => 6

[1,1,1,4] => [1,1,1,4] => [4,1,1,1] => 7

[1,1,4,1] => [1,1,4,1] => [4,1,1,1] => 7

[1,4,1,1] => [1,4,1,1] => [4,1,1,1] => 7

[4,1,1,1] => [4,1,1,1] => [4,1,1,1] => 7

[1,1,2,2] => [1,1,2,2] => [2,2,1,1] => 6

[1,2,1,2] => [1,2,1,2] => [2,2,1,1] => 6

[1,2,2,1] => [1,2,2,1] => [2,2,1,1] => 6

[2,1,1,2] => [2,1,1,2] => [2,2,1,1] => 6

[2,1,2,1] => [2,1,2,1] => [2,2,1,1] => 6

[2,2,1,1] => [2,2,1,1] => [2,2,1,1] => 6

[1,1,2,3] => [1,1,2,3] => [3,2,1,1] => 7

[1,1,3,2] => [1,1,3,2] => [3,2,1,1] => 7

[1,2,1,3] => [1,2,1,3] => [3,2,1,1] => 7

[1,2,3,1] => [1,2,3,1] => [3,2,1,1] => 7

[1,3,1,2] => [1,3,1,2] => [3,2,1,1] => 7

[1,3,2,1] => [1,3,2,1] => [3,2,1,1] => 7

[2,1,1,3] => [2,1,1,3] => [3,2,1,1] => 7

[2,1,3,1] => [2,1,3,1] => [3,2,1,1] => 7

[2,3,1,1] => [2,3,1,1] => [3,2,1,1] => 7

[3,1,1,2] => [3,1,1,2] => [3,2,1,1] => 7

[3,1,2,1] => [3,1,2,1] => [3,2,1,1] => 7

[3,2,1,1] => [3,2,1,1] => [3,2,1,1] => 7

[1,1,2,4] => [1,1,2,4] => [4,2,1,1] => 8

[1,1,4,2] => [1,1,4,2] => [4,2,1,1] => 8

[1,2,1,4] => [1,2,1,4] => [4,2,1,1] => 8

[1,2,4,1] => [1,2,4,1] => [4,2,1,1] => 8

[1,4,1,2] => [1,4,1,2] => [4,2,1,1] => 8

[1,4,2,1] => [1,4,2,1] => [4,2,1,1] => 8

[2,1,1,4] => [2,1,1,4] => [4,2,1,1] => 8

[2,1,4,1] => [2,1,4,1] => [4,2,1,1] => 8

[2,4,1,1] => [2,4,1,1] => [4,2,1,1] => 8

[4,1,1,2] => [4,1,1,2] => [4,2,1,1] => 8

[4,1,2,1] => [4,1,2,1] => [4,2,1,1] => 8

[4,2,1,1] => [4,2,1,1] => [4,2,1,1] => 8

[1,1,3,3] => [1,1,3,3] => [3,3,1,1] => 8

[1,3,1,3] => [1,3,1,3] => [3,3,1,1] => 8

[1,3,3,1] => [1,3,3,1] => [3,3,1,1] => 8

[3,1,1,3] => [3,1,1,3] => [3,3,1,1] => 8

[3,1,3,1] => [3,1,3,1] => [3,3,1,1] => 8

[3,3,1,1] => [3,3,1,1] => [3,3,1,1] => 8

[1,1,3,4] => [1,1,3,4] => [4,3,1,1] => 9

[1,1,4,3] => [1,1,4,3] => [4,3,1,1] => 9

[1,3,1,4] => [1,3,1,4] => [4,3,1,1] => 9

[1,3,4,1] => [1,3,4,1] => [4,3,1,1] => 9

[1,4,1,3] => [1,4,1,3] => [4,3,1,1] => 9

[1,4,3,1] => [1,4,3,1] => [4,3,1,1] => 9

[3,1,1,4] => [3,1,1,4] => [4,3,1,1] => 9

[3,1,4,1] => [3,1,4,1] => [4,3,1,1] => 9

[3,4,1,1] => [3,4,1,1] => [4,3,1,1] => 9

[4,1,1,3] => [4,1,1,3] => [4,3,1,1] => 9

[4,1,3,1] => [4,1,3,1] => [4,3,1,1] => 9

[4,3,1,1] => [4,3,1,1] => [4,3,1,1] => 9

[1,2,2,2] => [1,2,2,2] => [2,2,2,1] => 7

[2,1,2,2] => [2,1,2,2] => [2,2,2,1] => 7

[2,2,1,2] => [2,2,1,2] => [2,2,2,1] => 7

[2,2,2,1] => [2,2,2,1] => [2,2,2,1] => 7

[1,2,2,3] => [1,2,2,3] => [3,2,2,1] => 8

[1,2,3,2] => [1,2,3,2] => [3,2,2,1] => 8

[1,3,2,2] => [1,3,2,2] => [3,2,2,1] => 8

[2,1,2,3] => [2,1,2,3] => [3,2,2,1] => 8

[2,1,3,2] => [2,1,3,2] => [3,2,2,1] => 8

[2,2,1,3] => [2,2,1,3] => [3,2,2,1] => 8

[2,2,3,1] => [2,2,3,1] => [3,2,2,1] => 8

[2,3,1,2] => [2,3,1,2] => [3,2,2,1] => 8

[2,3,2,1] => [2,3,2,1] => [3,2,2,1] => 8

[3,1,2,2] => [3,1,2,2] => [3,2,2,1] => 8

[3,2,1,2] => [3,2,1,2] => [3,2,2,1] => 8

[3,2,2,1] => [3,2,2,1] => [3,2,2,1] => 8

[1,2,2,4] => [1,2,2,4] => [4,2,2,1] => 9

[1,2,4,2] => [1,2,4,2] => [4,2,2,1] => 9

[1,4,2,2] => [1,4,2,2] => [4,2,2,1] => 9

[2,1,2,4] => [2,1,2,4] => [4,2,2,1] => 9

>>> Load all 601 entries. <<<

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Description

The size of a partition.
This statistic is the constant statistic of the level sets.

Map

to composition

Description

Return the parking function interpreted as an integer composition.

Map

to partition

Description

Sends a composition to the partition obtained by sorting the entries.