- FindStat

Identifier

Mp00297: Parking functions —ordered tree⟶ Ordered trees
St000084: Ordered trees ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The number of subtrees.

Map

ordered tree

Description

The ordered tree associated with the parking function by Pollak.
Let $(p_1,\dots,p_n)$ be a parking function. Set $c_i = p_{i+1}-p_i \mod (n+1)$ to obtain a Prüfer code, and return the underlying ordered tree rooted at $0$.