- FindStat

Identifier

Mp00052: Parking functions —to non-decreasing parking function⟶ Parking functions
Mp00302: Parking functions —insertion tableau⟶ Semistandard tableaux
Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 5291 entries. <<<

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.

Map

insertion tableau

Description

The insertion tableau obtained by applying RSK to the parking function regarded as a word.

Map

catabolism

Description

Remove the first row of the semistandard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater or equal to than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than or equal to $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).