- FindStat

Identifier

Mp00305: Permutations —parking function⟶ Parking functions
St000165: Parking functions ⟶ ℤ

Values

=>
                            
                            
                            
                            
                            
                            

                        [1]=>[1]=>1
[1,2]=>[1,2]=>3
[2,1]=>[2,1]=>3
[1,2,3]=>[1,2,3]=>6
[1,3,2]=>[1,3,2]=>6
[2,1,3]=>[2,1,3]=>6
[2,3,1]=>[2,3,1]=>6
[3,1,2]=>[3,1,2]=>6
[3,2,1]=>[3,2,1]=>6
[1,2,3,4]=>[1,2,3,4]=>10
[1,2,4,3]=>[1,2,4,3]=>10
[1,3,2,4]=>[1,3,2,4]=>10
[1,3,4,2]=>[1,3,4,2]=>10
[1,4,2,3]=>[1,4,2,3]=>10
[1,4,3,2]=>[1,4,3,2]=>10
[2,1,3,4]=>[2,1,3,4]=>10
[2,1,4,3]=>[2,1,4,3]=>10
[2,3,1,4]=>[2,3,1,4]=>10
[2,3,4,1]=>[2,3,4,1]=>10
[2,4,1,3]=>[2,4,1,3]=>10
[2,4,3,1]=>[2,4,3,1]=>10
[3,1,2,4]=>[3,1,2,4]=>10
[3,1,4,2]=>[3,1,4,2]=>10
[3,2,1,4]=>[3,2,1,4]=>10
[3,2,4,1]=>[3,2,4,1]=>10
[3,4,1,2]=>[3,4,1,2]=>10
[3,4,2,1]=>[3,4,2,1]=>10
[4,1,2,3]=>[4,1,2,3]=>10
[4,1,3,2]=>[4,1,3,2]=>10
[4,2,1,3]=>[4,2,1,3]=>10
[4,2,3,1]=>[4,2,3,1]=>10
[4,3,1,2]=>[4,3,1,2]=>10
[4,3,2,1]=>[4,3,2,1]=>10
                    

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The sum of the entries of a parking function.
The generating function for parking functions by sum is the evaluation at $x=1$ and $y=1/q$ of the Tutte polynomial of the complete graph, multiplied by $q^\binom{n}{2}$.

Map

parking function

Description

Interpret the permutation as a parking function.