- FindStat

Identifier

Mp00299: Parking functions —ones to leading⟶ Parking functions
Mp00300: Parking functions —leading to ones⟶ Parking functions

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,2,1,3] => [1,2,1,4] => [1,2,1,3]

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

[1,3,1,2] => [1,4,1,2] => [1,3,1,2]

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

[2,1,1,3] => [1,3,1,4] => [2,1,1,3]

[2,1,3,1] => [2,4,2,1] => [2,1,3,1]

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

[3,1,1,2] => [1,4,1,3] => [3,1,1,2]

[3,1,2,1] => [2,1,4,2] => [3,1,2,1]

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

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

[1,1,4,2] => [2,2,3,1] => [1,1,4,2]

[1,2,1,4] => [1,1,2,3] => [1,2,1,4]

[1,2,4,1] => [1,3,2,1] => [1,2,4,1]

[1,4,1,2] => [2,1,2,3] => [1,4,1,2]

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

[2,1,1,4] => [1,1,3,2] => [2,1,1,4]

[2,1,4,1] => [1,2,3,1] => [2,1,4,1]

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

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

[4,1,2,1] => [1,4,3,1] => [4,1,2,1]

[4,2,1,1] => [1,3,4,1] => [4,2,1,1]

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

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

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

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

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

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

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

[1,1,4,3] => [2,2,4,1] => [1,1,4,3]

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

[1,3,4,1] => [2,2,1,4] => [1,3,4,1]

[1,4,1,3] => [3,3,1,2] => [1,4,1,3]

[1,4,3,1] => [3,3,2,1] => [1,4,3,1]

[3,1,1,4] => [1,1,4,2] => [3,1,1,4]

[3,1,4,1] => [2,2,1,3] => [3,1,4,1]

[3,4,1,1] => [2,3,1,2] => [3,4,1,1]

[4,1,1,3] => [3,2,3,1] => [4,1,1,3]

[4,1,3,1] => [3,1,3,2] => [4,1,3,1]

[4,3,1,1] => [2,4,1,2] => [4,3,1,1]

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

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

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

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

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

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

[1,3,2,2] => [1,2,4,2] => [1,3,2,2]

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

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

[2,2,1,3] => [3,1,1,4] => [2,2,1,3]

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

[2,3,1,2] => [3,1,4,1] => [2,3,1,2]

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

[3,1,2,2] => [4,1,2,1] => [3,1,2,2]

[3,2,1,2] => [4,2,1,2] => [3,2,1,2]

[3,2,2,1] => [2,1,4,1] => [3,2,2,1]

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

[1,2,4,2] => [2,3,3,1] => [1,2,4,2]

[1,4,2,2] => [2,3,1,3] => [1,4,2,2]

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

>>> Load all 18248 entries. <<<

Map

ones to leading

Description

The unique parking function obtained by applying the Foata-Riordan map to obtain a Prüfer code, then prepending 0 and cyclically shifting.
Let $c_1,\dots,c_{n-1}$ be the Prüfer code obtained via the Foata-Riordan map described in [1, eq (1.2)] and let $c_0=0$. This map returns the unique parking function $(q_1,\dots,q_n)$ such that $q_i-c_{i-1}$ is constant modulo $n+1$, see [2, sec 4].
This map sends the number of ones to the number of occurrences of the first element.

Map

leading to ones

Description

The unique parking function obtained by subtracting the first entry from all others to obtain a Prüfer code and then applying the inverse of the Foata-Riordan map.
This map is the inverse of Mp00299ones to leading.