- FindStat

edit this statistic or download as text // json

Identifier

St001903: Parking functions ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>1
[1,1]=>1
[1,2]=>2
[2,1]=>0
[1,1,1]=>1
[1,1,2]=>1
[1,2,1]=>2
[2,1,1]=>0
[1,1,3]=>2
[1,3,1]=>1
[3,1,1]=>0
[1,2,2]=>2
[2,1,2]=>0
[2,2,1]=>1
[1,2,3]=>3
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>1
[1,1,1,1]=>1
[1,1,1,2]=>1
[1,1,2,1]=>1
[1,2,1,1]=>2
[2,1,1,1]=>0
[1,1,1,3]=>1
[1,1,3,1]=>2
[1,3,1,1]=>1
[3,1,1,1]=>0
[1,1,1,4]=>2
[1,1,4,1]=>1
[1,4,1,1]=>1
[4,1,1,1]=>0
[1,1,2,2]=>1
[1,2,1,2]=>2
[1,2,2,1]=>2
[2,1,1,2]=>0
[2,1,2,1]=>0
[2,2,1,1]=>1
[1,1,2,3]=>1
[1,1,3,2]=>2
[1,2,1,3]=>2
[1,2,3,1]=>3
[1,3,1,2]=>1
[1,3,2,1]=>1
[2,1,1,3]=>0
[2,1,3,1]=>1
[2,3,1,1]=>0
[3,1,1,2]=>0
[3,1,2,1]=>0
[3,2,1,1]=>1
[1,1,2,4]=>2
[1,1,4,2]=>1
[1,2,1,4]=>3
[1,2,4,1]=>2
[1,4,1,2]=>1
[1,4,2,1]=>1
[2,1,1,4]=>1
[2,1,4,1]=>0
[2,4,1,1]=>0
[4,1,1,2]=>0
[4,1,2,1]=>0
[4,2,1,1]=>1
[1,1,3,3]=>2
[1,3,1,3]=>1
[1,3,3,1]=>2
[3,1,1,3]=>0
[3,1,3,1]=>1
[3,3,1,1]=>0
[1,1,3,4]=>3
[1,1,4,3]=>1
[1,3,1,4]=>2
[1,3,4,1]=>1
[1,4,1,3]=>1
[1,4,3,1]=>2
[3,1,1,4]=>1
[3,1,4,1]=>0
[3,4,1,1]=>0
[4,1,1,3]=>0
[4,1,3,1]=>1
[4,3,1,1]=>0
[1,2,2,2]=>2
[2,1,2,2]=>0
[2,2,1,2]=>1
[2,2,2,1]=>1
[1,2,2,3]=>2
[1,2,3,2]=>3
[1,3,2,2]=>1
[2,1,2,3]=>0
[2,1,3,2]=>1
[2,2,1,3]=>1
[2,2,3,1]=>2
[2,3,1,2]=>0
[2,3,2,1]=>0
[3,1,2,2]=>0
[3,2,1,2]=>1
[3,2,2,1]=>1
[1,2,2,4]=>3
[1,2,4,2]=>2
[1,4,2,2]=>1
[2,1,2,4]=>1
[2,1,4,2]=>0
[2,2,1,4]=>2
[2,2,4,1]=>1
[2,4,1,2]=>0
[2,4,2,1]=>0
[4,1,2,2]=>0
[4,2,1,2]=>1
[4,2,2,1]=>1
[1,2,3,3]=>3
[1,3,2,3]=>1
[1,3,3,2]=>2
[2,1,3,3]=>1
[2,3,1,3]=>0
[2,3,3,1]=>1
[3,1,2,3]=>0
[3,1,3,2]=>1
[3,2,1,3]=>1
[3,2,3,1]=>2
[3,3,1,2]=>0
[3,3,2,1]=>0
[1,2,3,4]=>4
[1,2,4,3]=>2
[1,3,2,4]=>2
[1,3,4,2]=>1
[1,4,2,3]=>1
[1,4,3,2]=>2
[2,1,3,4]=>2
[2,1,4,3]=>0
[2,3,1,4]=>1
[2,3,4,1]=>0
[2,4,1,3]=>0
[2,4,3,1]=>1
[3,1,2,4]=>1
[3,1,4,2]=>0
[3,2,1,4]=>2
[3,2,4,1]=>1
[3,4,1,2]=>0
[3,4,2,1]=>0
[4,1,2,3]=>0
[4,1,3,2]=>1
[4,2,1,3]=>1
[4,2,3,1]=>2
[4,3,1,2]=>0
[4,3,2,1]=>0
[1,1,1,1,1]=>1
[1,1,1,1,2]=>1
[1,1,1,2,1]=>1
[1,1,2,1,1]=>1
[1,2,1,1,1]=>2
[2,1,1,1,1]=>0
[1,1,1,1,3]=>1
[1,1,1,3,1]=>1
[1,1,3,1,1]=>2
[1,3,1,1,1]=>1
[3,1,1,1,1]=>0
[1,1,1,1,4]=>1
[1,1,1,4,1]=>2
[1,1,4,1,1]=>1
[1,4,1,1,1]=>1
[4,1,1,1,1]=>0
[1,1,1,1,5]=>2
[1,1,1,5,1]=>1
[1,1,5,1,1]=>1
[1,5,1,1,1]=>1
[5,1,1,1,1]=>0
[1,1,1,2,2]=>1
[1,1,2,1,2]=>1
[1,1,2,2,1]=>1
[1,2,1,1,2]=>2
[1,2,1,2,1]=>2
[1,2,2,1,1]=>2
[2,1,1,1,2]=>0
[2,1,1,2,1]=>0
[2,1,2,1,1]=>0
[2,2,1,1,1]=>1
[1,1,1,2,3]=>1
[1,1,1,3,2]=>1
[1,1,2,1,3]=>1
[1,1,2,3,1]=>1
[1,1,3,1,2]=>2
[1,1,3,2,1]=>2
[1,2,1,1,3]=>2
[1,2,1,3,1]=>2
[1,2,3,1,1]=>3
[1,3,1,1,2]=>1
[1,3,1,2,1]=>1
[1,3,2,1,1]=>1
[2,1,1,1,3]=>0
[2,1,1,3,1]=>0
[2,1,3,1,1]=>1
[2,3,1,1,1]=>0
[3,1,1,1,2]=>0
[3,1,1,2,1]=>0
[3,1,2,1,1]=>0
[3,2,1,1,1]=>1
[1,1,1,2,4]=>1
[1,1,1,4,2]=>2
[1,1,2,1,4]=>1
[1,1,2,4,1]=>2
[1,1,4,1,2]=>1
[1,1,4,2,1]=>1
[1,2,1,1,4]=>2
[1,2,1,4,1]=>3
[1,2,4,1,1]=>2
[1,4,1,1,2]=>1
[1,4,1,2,1]=>1
[1,4,2,1,1]=>1
[2,1,1,1,4]=>0
[2,1,1,4,1]=>1
[2,1,4,1,1]=>0
[2,4,1,1,1]=>0
[4,1,1,1,2]=>0
[4,1,1,2,1]=>0
[4,1,2,1,1]=>0
[4,2,1,1,1]=>1
[1,1,1,2,5]=>2
[1,1,1,5,2]=>1
[1,1,2,1,5]=>2
[1,1,2,5,1]=>1
[1,1,5,1,2]=>1
[1,1,5,2,1]=>1
[1,2,1,1,5]=>3
[1,2,1,5,1]=>2
[1,2,5,1,1]=>2
[1,5,1,1,2]=>1
[1,5,1,2,1]=>1
[1,5,2,1,1]=>1
[2,1,1,1,5]=>1
[2,1,1,5,1]=>0
[2,1,5,1,1]=>0
[2,5,1,1,1]=>0
[5,1,1,1,2]=>0
[5,1,1,2,1]=>0
[5,1,2,1,1]=>0
[5,2,1,1,1]=>1
[1,1,1,3,3]=>1
[1,1,3,1,3]=>2
[1,1,3,3,1]=>2
[1,3,1,1,3]=>1
[1,3,1,3,1]=>1
[1,3,3,1,1]=>2
[3,1,1,1,3]=>0
[3,1,1,3,1]=>0
[3,1,3,1,1]=>1
[3,3,1,1,1]=>0
[1,1,1,3,4]=>1
[1,1,1,4,3]=>2
[1,1,3,1,4]=>2
[1,1,3,4,1]=>3
[1,1,4,1,3]=>1
[1,1,4,3,1]=>1
[1,3,1,1,4]=>1
[1,3,1,4,1]=>2
[1,3,4,1,1]=>1
[1,4,1,1,3]=>1
[1,4,1,3,1]=>1
[1,4,3,1,1]=>2
[3,1,1,1,4]=>0
[3,1,1,4,1]=>1
[3,1,4,1,1]=>0
[3,4,1,1,1]=>0
[4,1,1,1,3]=>0
[4,1,1,3,1]=>0
[4,1,3,1,1]=>1
[4,3,1,1,1]=>0
[1,1,1,3,5]=>2
[1,1,1,5,3]=>1
[1,1,3,1,5]=>3
[1,1,3,5,1]=>2
[1,1,5,1,3]=>1
[1,1,5,3,1]=>1
[1,3,1,1,5]=>2
[1,3,1,5,1]=>1
[1,3,5,1,1]=>1
[1,5,1,1,3]=>1
[1,5,1,3,1]=>1
[1,5,3,1,1]=>2
[3,1,1,1,5]=>1
[3,1,1,5,1]=>0
[3,1,5,1,1]=>0
[3,5,1,1,1]=>0
[5,1,1,1,3]=>0
[5,1,1,3,1]=>0
[5,1,3,1,1]=>1
[5,3,1,1,1]=>0
[1,1,1,4,4]=>2
[1,1,4,1,4]=>1
[1,1,4,4,1]=>2
[1,4,1,1,4]=>1
[1,4,1,4,1]=>2
[1,4,4,1,1]=>1
[4,1,1,1,4]=>0
[4,1,1,4,1]=>1
[4,1,4,1,1]=>0
[4,4,1,1,1]=>0
[1,1,1,4,5]=>3
[1,1,1,5,4]=>1
[1,1,4,1,5]=>2
[1,1,4,5,1]=>1
[1,1,5,1,4]=>1
[1,1,5,4,1]=>2
[1,4,1,1,5]=>2
[1,4,1,5,1]=>1
[1,4,5,1,1]=>1
[1,5,1,1,4]=>1
[1,5,1,4,1]=>2
[1,5,4,1,1]=>1
[4,1,1,1,5]=>1
[4,1,1,5,1]=>0
[4,1,5,1,1]=>0
[4,5,1,1,1]=>0
[5,1,1,1,4]=>0
[5,1,1,4,1]=>1
[5,1,4,1,1]=>0
[5,4,1,1,1]=>0
[1,1,2,2,2]=>1
[1,2,1,2,2]=>2
[1,2,2,1,2]=>2
[1,2,2,2,1]=>2
[2,1,1,2,2]=>0
[2,1,2,1,2]=>0
[2,1,2,2,1]=>0
[2,2,1,1,2]=>1
[2,2,1,2,1]=>1
[2,2,2,1,1]=>1
[1,1,2,2,3]=>1
[1,1,2,3,2]=>1
[1,1,3,2,2]=>2
[1,2,1,2,3]=>2
[1,2,1,3,2]=>2
[1,2,2,1,3]=>2
[1,2,2,3,1]=>2
[1,2,3,1,2]=>3
[1,2,3,2,1]=>3
[1,3,1,2,2]=>1
[1,3,2,1,2]=>1
[1,3,2,2,1]=>1
[2,1,1,2,3]=>0
[2,1,1,3,2]=>0
[2,1,2,1,3]=>0
[2,1,2,3,1]=>0
[2,1,3,1,2]=>1
[2,1,3,2,1]=>1
[2,2,1,1,3]=>1
[2,2,1,3,1]=>1
[2,2,3,1,1]=>2
[2,3,1,1,2]=>0
[2,3,1,2,1]=>0
[2,3,2,1,1]=>0
[3,1,1,2,2]=>0
[3,1,2,1,2]=>0
[3,1,2,2,1]=>0
[3,2,1,1,2]=>1
[3,2,1,2,1]=>1
[3,2,2,1,1]=>1
[1,1,2,2,4]=>1
[1,1,2,4,2]=>2
[1,1,4,2,2]=>1
[1,2,1,2,4]=>2
[1,2,1,4,2]=>3
[1,2,2,1,4]=>2
[1,2,2,4,1]=>3
[1,2,4,1,2]=>2
[1,2,4,2,1]=>2
[1,4,1,2,2]=>1
[1,4,2,1,2]=>1
[1,4,2,2,1]=>1
[2,1,1,2,4]=>0
[2,1,1,4,2]=>1
[2,1,2,1,4]=>0
[2,1,2,4,1]=>1
[2,1,4,1,2]=>0
[2,1,4,2,1]=>0
[2,2,1,1,4]=>1
[2,2,1,4,1]=>2
[2,2,4,1,1]=>1
[2,4,1,1,2]=>0
[2,4,1,2,1]=>0
[2,4,2,1,1]=>0
[4,1,1,2,2]=>0
[4,1,2,1,2]=>0
[4,1,2,2,1]=>0
[4,2,1,1,2]=>1
[4,2,1,2,1]=>1
[4,2,2,1,1]=>1
[1,1,2,2,5]=>2
[1,1,2,5,2]=>1
[1,1,5,2,2]=>1
[1,2,1,2,5]=>3
[1,2,1,5,2]=>2
[1,2,2,1,5]=>3
[1,2,2,5,1]=>2
[1,2,5,1,2]=>2
[1,2,5,2,1]=>2
[1,5,1,2,2]=>1
[1,5,2,1,2]=>1
[1,5,2,2,1]=>1
[2,1,1,2,5]=>1
[2,1,1,5,2]=>0
[2,1,2,1,5]=>1
[2,1,2,5,1]=>0
[2,1,5,1,2]=>0
[2,1,5,2,1]=>0
[2,2,1,1,5]=>2
[2,2,1,5,1]=>1
[2,2,5,1,1]=>1
[2,5,1,1,2]=>0
[2,5,1,2,1]=>0
[2,5,2,1,1]=>0
[5,1,1,2,2]=>0
[5,1,2,1,2]=>0
[5,1,2,2,1]=>0
[5,2,1,1,2]=>1
[5,2,1,2,1]=>1
[5,2,2,1,1]=>1
[1,1,2,3,3]=>1
[1,1,3,2,3]=>2
[1,1,3,3,2]=>2
[1,2,1,3,3]=>2
[1,2,3,1,3]=>3
[1,2,3,3,1]=>3
[1,3,1,2,3]=>1
[1,3,1,3,2]=>1
[1,3,2,1,3]=>1
[1,3,2,3,1]=>1
[1,3,3,1,2]=>2
[1,3,3,2,1]=>2
[2,1,1,3,3]=>0
[2,1,3,1,3]=>1
[2,1,3,3,1]=>1
[2,3,1,1,3]=>0
[2,3,1,3,1]=>0
[2,3,3,1,1]=>1
[3,1,1,2,3]=>0
[3,1,1,3,2]=>0
[3,1,2,1,3]=>0
[3,1,2,3,1]=>0
[3,1,3,1,2]=>1
[3,1,3,2,1]=>1
[3,2,1,1,3]=>1
[3,2,1,3,1]=>1
[3,2,3,1,1]=>2
[3,3,1,1,2]=>0
[3,3,1,2,1]=>0
[3,3,2,1,1]=>0
[1,1,2,3,4]=>1
[1,1,2,4,3]=>2
[1,1,3,2,4]=>2
[1,1,3,4,2]=>3
[1,1,4,2,3]=>1
[1,1,4,3,2]=>1
[1,2,1,3,4]=>2
[1,2,1,4,3]=>3
[1,2,3,1,4]=>3
[1,2,3,4,1]=>4
[1,2,4,1,3]=>2
[1,2,4,3,1]=>2
[1,3,1,2,4]=>1
[1,3,1,4,2]=>2
[1,3,2,1,4]=>1
[1,3,2,4,1]=>2
[1,3,4,1,2]=>1
[1,3,4,2,1]=>1
[1,4,1,2,3]=>1
[1,4,1,3,2]=>1
[1,4,2,1,3]=>1
[1,4,2,3,1]=>1
[1,4,3,1,2]=>2
[1,4,3,2,1]=>2
[2,1,1,3,4]=>0
[2,1,1,4,3]=>1
[2,1,3,1,4]=>1
[2,1,3,4,1]=>2
[2,1,4,1,3]=>0
[2,1,4,3,1]=>0
[2,3,1,1,4]=>0
[2,3,1,4,1]=>1
[2,3,4,1,1]=>0
[2,4,1,1,3]=>0
[2,4,1,3,1]=>0
[2,4,3,1,1]=>1
[3,1,1,2,4]=>0
[3,1,1,4,2]=>1
[3,1,2,1,4]=>0
[3,1,2,4,1]=>1
[3,1,4,1,2]=>0
[3,1,4,2,1]=>0
[3,2,1,1,4]=>1
[3,2,1,4,1]=>2
[3,2,4,1,1]=>1
[3,4,1,1,2]=>0
[3,4,1,2,1]=>0
[3,4,2,1,1]=>0
[4,1,1,2,3]=>0
[4,1,1,3,2]=>0
[4,1,2,1,3]=>0
[4,1,2,3,1]=>0
[4,1,3,1,2]=>1
[4,1,3,2,1]=>1
[4,2,1,1,3]=>1
[4,2,1,3,1]=>1
[4,2,3,1,1]=>2
[4,3,1,1,2]=>0
[4,3,1,2,1]=>0
[4,3,2,1,1]=>0
[1,1,2,3,5]=>2
[1,1,2,5,3]=>1
[1,1,3,2,5]=>3
[1,1,3,5,2]=>2
[1,1,5,2,3]=>1
[1,1,5,3,2]=>1
[1,2,1,3,5]=>3
[1,2,1,5,3]=>2
[1,2,3,1,5]=>4
[1,2,3,5,1]=>3
[1,2,5,1,3]=>2
[1,2,5,3,1]=>2
[1,3,1,2,5]=>2
[1,3,1,5,2]=>1
[1,3,2,1,5]=>2
[1,3,2,5,1]=>1
[1,3,5,1,2]=>1
[1,3,5,2,1]=>1
[1,5,1,2,3]=>1
[1,5,1,3,2]=>1
[1,5,2,1,3]=>1
[1,5,2,3,1]=>1
[1,5,3,1,2]=>2
[1,5,3,2,1]=>2
[2,1,1,3,5]=>1
[2,1,1,5,3]=>0
[2,1,3,1,5]=>2
[2,1,3,5,1]=>1
[2,1,5,1,3]=>0
[2,1,5,3,1]=>0
[2,3,1,1,5]=>1
[2,3,1,5,1]=>0
[2,3,5,1,1]=>0
[2,5,1,1,3]=>0
[2,5,1,3,1]=>0
[2,5,3,1,1]=>1
[3,1,1,2,5]=>1
[3,1,1,5,2]=>0
[3,1,2,1,5]=>1
[3,1,2,5,1]=>0
[3,1,5,1,2]=>0
[3,1,5,2,1]=>0
[3,2,1,1,5]=>2
[3,2,1,5,1]=>1
[3,2,5,1,1]=>1
[3,5,1,1,2]=>0
[3,5,1,2,1]=>0
[3,5,2,1,1]=>0
[5,1,1,2,3]=>0
[5,1,1,3,2]=>0
[5,1,2,1,3]=>0
[5,1,2,3,1]=>0
[5,1,3,1,2]=>1
[5,1,3,2,1]=>1
[5,2,1,1,3]=>1
[5,2,1,3,1]=>1
[5,2,3,1,1]=>2
[5,3,1,1,2]=>0
[5,3,1,2,1]=>0
[5,3,2,1,1]=>0
[1,1,2,4,4]=>2
[1,1,4,2,4]=>1
[1,1,4,4,2]=>2
[1,2,1,4,4]=>3
[1,2,4,1,4]=>2
[1,2,4,4,1]=>3
[1,4,1,2,4]=>1
[1,4,1,4,2]=>2
[1,4,2,1,4]=>1
[1,4,2,4,1]=>2
[1,4,4,1,2]=>1
[1,4,4,2,1]=>1
[2,1,1,4,4]=>1
[2,1,4,1,4]=>0
[2,1,4,4,1]=>1
[2,4,1,1,4]=>0
[2,4,1,4,1]=>1
[2,4,4,1,1]=>0
[4,1,1,2,4]=>0
[4,1,1,4,2]=>1
[4,1,2,1,4]=>0
[4,1,2,4,1]=>1
[4,1,4,1,2]=>0
[4,1,4,2,1]=>0
[4,2,1,1,4]=>1
[4,2,1,4,1]=>2
[4,2,4,1,1]=>1
[4,4,1,1,2]=>0
[4,4,1,2,1]=>0
[4,4,2,1,1]=>0
[1,1,2,4,5]=>3
[1,1,2,5,4]=>1
[1,1,4,2,5]=>2
[1,1,4,5,2]=>1
[1,1,5,2,4]=>1
[1,1,5,4,2]=>2
[1,2,1,4,5]=>4
[1,2,1,5,4]=>2
[1,2,4,1,5]=>3
[1,2,4,5,1]=>2
[1,2,5,1,4]=>2
[1,2,5,4,1]=>3
[1,4,1,2,5]=>2
[1,4,1,5,2]=>1
[1,4,2,1,5]=>2
[1,4,2,5,1]=>1
[1,4,5,1,2]=>1
[1,4,5,2,1]=>1
[1,5,1,2,4]=>1
[1,5,1,4,2]=>2
[1,5,2,1,4]=>1
[1,5,2,4,1]=>2
[1,5,4,1,2]=>1
[1,5,4,2,1]=>1
[2,1,1,4,5]=>2
[2,1,1,5,4]=>0
[2,1,4,1,5]=>1
[2,1,4,5,1]=>0
[2,1,5,1,4]=>0
[2,1,5,4,1]=>1
[2,4,1,1,5]=>1
[2,4,1,5,1]=>0
[2,4,5,1,1]=>0
[2,5,1,1,4]=>0
[2,5,1,4,1]=>1
[2,5,4,1,1]=>0
[4,1,1,2,5]=>1
[4,1,1,5,2]=>0
[4,1,2,1,5]=>1
[4,1,2,5,1]=>0
[4,1,5,1,2]=>0
[4,1,5,2,1]=>0
[4,2,1,1,5]=>2
[4,2,1,5,1]=>1
[4,2,5,1,1]=>1
[4,5,1,1,2]=>0
[4,5,1,2,1]=>0
[4,5,2,1,1]=>0
[5,1,1,2,4]=>0
[5,1,1,4,2]=>1
[5,1,2,1,4]=>0
[5,1,2,4,1]=>1
[5,1,4,1,2]=>0
[5,1,4,2,1]=>0
[5,2,1,1,4]=>1
[5,2,1,4,1]=>2
[5,2,4,1,1]=>1
[5,4,1,1,2]=>0
[5,4,1,2,1]=>0
[5,4,2,1,1]=>0
[1,1,3,3,3]=>2
[1,3,1,3,3]=>1
[1,3,3,1,3]=>2
[1,3,3,3,1]=>2
[3,1,1,3,3]=>0
[3,1,3,1,3]=>1
[3,1,3,3,1]=>1
[3,3,1,1,3]=>0
[3,3,1,3,1]=>0
[3,3,3,1,1]=>1
[1,1,3,3,4]=>2
[1,1,3,4,3]=>3
[1,1,4,3,3]=>1
[1,3,1,3,4]=>1
[1,3,1,4,3]=>2
[1,3,3,1,4]=>2
[1,3,3,4,1]=>3
[1,3,4,1,3]=>1
[1,3,4,3,1]=>1
[1,4,1,3,3]=>1
[1,4,3,1,3]=>2
[1,4,3,3,1]=>2
[3,1,1,3,4]=>0
[3,1,1,4,3]=>1
[3,1,3,1,4]=>1
[3,1,3,4,1]=>2
[3,1,4,1,3]=>0
[3,1,4,3,1]=>0
[3,3,1,1,4]=>0
[3,3,1,4,1]=>1
[3,3,4,1,1]=>0
[3,4,1,1,3]=>0
[3,4,1,3,1]=>0
[3,4,3,1,1]=>1
[4,1,1,3,3]=>0
[4,1,3,1,3]=>1
[4,1,3,3,1]=>1
[4,3,1,1,3]=>0
[4,3,1,3,1]=>0
[4,3,3,1,1]=>1
[1,1,3,3,5]=>3
[1,1,3,5,3]=>2
[1,1,5,3,3]=>1
[1,3,1,3,5]=>2
[1,3,1,5,3]=>1
[1,3,3,1,5]=>3
[1,3,3,5,1]=>2
[1,3,5,1,3]=>1
[1,3,5,3,1]=>1
[1,5,1,3,3]=>1
[1,5,3,1,3]=>2
[1,5,3,3,1]=>2
[3,1,1,3,5]=>1
[3,1,1,5,3]=>0
[3,1,3,1,5]=>2
[3,1,3,5,1]=>1
[3,1,5,1,3]=>0
[3,1,5,3,1]=>0
[3,3,1,1,5]=>1
[3,3,1,5,1]=>0
[3,3,5,1,1]=>0
[3,5,1,1,3]=>0
[3,5,1,3,1]=>0
[3,5,3,1,1]=>1
[5,1,1,3,3]=>0
[5,1,3,1,3]=>1
[5,1,3,3,1]=>1
[5,3,1,1,3]=>0
[5,3,1,3,1]=>0
[5,3,3,1,1]=>1
[1,1,3,4,4]=>3
[1,1,4,3,4]=>1
[1,1,4,4,3]=>2
[1,3,1,4,4]=>2
[1,3,4,1,4]=>1
[1,3,4,4,1]=>2
[1,4,1,3,4]=>1
[1,4,1,4,3]=>2
[1,4,3,1,4]=>2
[1,4,3,4,1]=>3
[1,4,4,1,3]=>1
[1,4,4,3,1]=>1
[3,1,1,4,4]=>1
[3,1,4,1,4]=>0
[3,1,4,4,1]=>1
[3,4,1,1,4]=>0
[3,4,1,4,1]=>1
[3,4,4,1,1]=>0
[4,1,1,3,4]=>0
[4,1,1,4,3]=>1
[4,1,3,1,4]=>1
[4,1,3,4,1]=>2
[4,1,4,1,3]=>0
[4,1,4,3,1]=>0
[4,3,1,1,4]=>0
[4,3,1,4,1]=>1
[4,3,4,1,1]=>0
[4,4,1,1,3]=>0
[4,4,1,3,1]=>0
[4,4,3,1,1]=>1
[1,1,3,4,5]=>4
[1,1,3,5,4]=>2
[1,1,4,3,5]=>2
[1,1,4,5,3]=>1
[1,1,5,3,4]=>1
[1,1,5,4,3]=>2
[1,3,1,4,5]=>3
[1,3,1,5,4]=>1
[1,3,4,1,5]=>2
[1,3,4,5,1]=>1
[1,3,5,1,4]=>1
[1,3,5,4,1]=>2
[1,4,1,3,5]=>2
[1,4,1,5,3]=>1
[1,4,3,1,5]=>3
[1,4,3,5,1]=>2
[1,4,5,1,3]=>1
[1,4,5,3,1]=>1
[1,5,1,3,4]=>1
[1,5,1,4,3]=>2
[1,5,3,1,4]=>2
[1,5,3,4,1]=>3
[1,5,4,1,3]=>1
[1,5,4,3,1]=>1
[3,1,1,4,5]=>2
[3,1,1,5,4]=>0
[3,1,4,1,5]=>1
[3,1,4,5,1]=>0
[3,1,5,1,4]=>0
[3,1,5,4,1]=>1
[3,4,1,1,5]=>1
[3,4,1,5,1]=>0
[3,4,5,1,1]=>0
[3,5,1,1,4]=>0
[3,5,1,4,1]=>1
[3,5,4,1,1]=>0
[4,1,1,3,5]=>1
[4,1,1,5,3]=>0
[4,1,3,1,5]=>2
[4,1,3,5,1]=>1
[4,1,5,1,3]=>0
[4,1,5,3,1]=>0
[4,3,1,1,5]=>1
[4,3,1,5,1]=>0
[4,3,5,1,1]=>0
[4,5,1,1,3]=>0
[4,5,1,3,1]=>0
[4,5,3,1,1]=>1
[5,1,1,3,4]=>0
[5,1,1,4,3]=>1
[5,1,3,1,4]=>1
[5,1,3,4,1]=>2
[5,1,4,1,3]=>0
[5,1,4,3,1]=>0
[5,3,1,1,4]=>0
[5,3,1,4,1]=>1
[5,3,4,1,1]=>0
[5,4,1,1,3]=>0
[5,4,1,3,1]=>0
[5,4,3,1,1]=>1
[1,2,2,2,2]=>2
[2,1,2,2,2]=>0
[2,2,1,2,2]=>1
[2,2,2,1,2]=>1
[2,2,2,2,1]=>1
[1,2,2,2,3]=>2
[1,2,2,3,2]=>2
[1,2,3,2,2]=>3
[1,3,2,2,2]=>1
[2,1,2,2,3]=>0
[2,1,2,3,2]=>0
[2,1,3,2,2]=>1
[2,2,1,2,3]=>1
[2,2,1,3,2]=>1
[2,2,2,1,3]=>1
[2,2,2,3,1]=>1
[2,2,3,1,2]=>2
[2,2,3,2,1]=>2
[2,3,1,2,2]=>0
[2,3,2,1,2]=>0
[2,3,2,2,1]=>0
[3,1,2,2,2]=>0
[3,2,1,2,2]=>1
[3,2,2,1,2]=>1
[3,2,2,2,1]=>1
[1,2,2,2,4]=>2
[1,2,2,4,2]=>3
[1,2,4,2,2]=>2
[1,4,2,2,2]=>1
[2,1,2,2,4]=>0
[2,1,2,4,2]=>1
[2,1,4,2,2]=>0
[2,2,1,2,4]=>1
[2,2,1,4,2]=>2
[2,2,2,1,4]=>1
[2,2,2,4,1]=>2
[2,2,4,1,2]=>1
[2,2,4,2,1]=>1
[2,4,1,2,2]=>0
[2,4,2,1,2]=>0
[2,4,2,2,1]=>0
[4,1,2,2,2]=>0
[4,2,1,2,2]=>1
[4,2,2,1,2]=>1
[4,2,2,2,1]=>1
[1,2,2,2,5]=>3
[1,2,2,5,2]=>2
[1,2,5,2,2]=>2
[1,5,2,2,2]=>1
[2,1,2,2,5]=>1
[2,1,2,5,2]=>0
[2,1,5,2,2]=>0
[2,2,1,2,5]=>2
[2,2,1,5,2]=>1
[2,2,2,1,5]=>2
[2,2,2,5,1]=>1
[2,2,5,1,2]=>1
[2,2,5,2,1]=>1
[2,5,1,2,2]=>0
[2,5,2,1,2]=>0
[2,5,2,2,1]=>0
[5,1,2,2,2]=>0
[5,2,1,2,2]=>1
[5,2,2,1,2]=>1
[5,2,2,2,1]=>1
[1,2,2,3,3]=>2
[1,2,3,2,3]=>3
[1,2,3,3,2]=>3
[1,3,2,2,3]=>1
[1,3,2,3,2]=>1
[1,3,3,2,2]=>2
[2,1,2,3,3]=>0
[2,1,3,2,3]=>1
[2,1,3,3,2]=>1
[2,2,1,3,3]=>1
[2,2,3,1,3]=>2
[2,2,3,3,1]=>2
[2,3,1,2,3]=>0
[2,3,1,3,2]=>0
[2,3,2,1,3]=>0
[2,3,2,3,1]=>0
[2,3,3,1,2]=>1
[2,3,3,2,1]=>1
[3,1,2,2,3]=>0
[3,1,2,3,2]=>0
[3,1,3,2,2]=>1
[3,2,1,2,3]=>1
[3,2,1,3,2]=>1
[3,2,2,1,3]=>1
[3,2,2,3,1]=>1
[3,2,3,1,2]=>2
[3,2,3,2,1]=>2
[3,3,1,2,2]=>0
[3,3,2,1,2]=>0
[3,3,2,2,1]=>0
[1,2,2,3,4]=>2
[1,2,2,4,3]=>3
[1,2,3,2,4]=>3
[1,2,3,4,2]=>4
[1,2,4,2,3]=>2
[1,2,4,3,2]=>2
[1,3,2,2,4]=>1
[1,3,2,4,2]=>2
[1,3,4,2,2]=>1
[1,4,2,2,3]=>1
[1,4,2,3,2]=>1
[1,4,3,2,2]=>2
[2,1,2,3,4]=>0
[2,1,2,4,3]=>1
[2,1,3,2,4]=>1
[2,1,3,4,2]=>2
[2,1,4,2,3]=>0
[2,1,4,3,2]=>0
[2,2,1,3,4]=>1
[2,2,1,4,3]=>2
[2,2,3,1,4]=>2
[2,2,3,4,1]=>3
[2,2,4,1,3]=>1
[2,2,4,3,1]=>1
[2,3,1,2,4]=>0
[2,3,1,4,2]=>1
[2,3,2,1,4]=>0
[2,3,2,4,1]=>1
[2,3,4,1,2]=>0
[2,3,4,2,1]=>0
[2,4,1,2,3]=>0
[2,4,1,3,2]=>0
[2,4,2,1,3]=>0
[2,4,2,3,1]=>0
[2,4,3,1,2]=>1
[2,4,3,2,1]=>1
[3,1,2,2,4]=>0
[3,1,2,4,2]=>1
[3,1,4,2,2]=>0
[3,2,1,2,4]=>1
[3,2,1,4,2]=>2
[3,2,2,1,4]=>1
[3,2,2,4,1]=>2
[3,2,4,1,2]=>1
[3,2,4,2,1]=>1
[3,4,1,2,2]=>0
[3,4,2,1,2]=>0
[3,4,2,2,1]=>0
[4,1,2,2,3]=>0
[4,1,2,3,2]=>0
[4,1,3,2,2]=>1
[4,2,1,2,3]=>1
[4,2,1,3,2]=>1
[4,2,2,1,3]=>1
[4,2,2,3,1]=>1
[4,2,3,1,2]=>2
[4,2,3,2,1]=>2
[4,3,1,2,2]=>0
[4,3,2,1,2]=>0
[4,3,2,2,1]=>0
[1,2,2,3,5]=>3
[1,2,2,5,3]=>2
[1,2,3,2,5]=>4
[1,2,3,5,2]=>3
[1,2,5,2,3]=>2
[1,2,5,3,2]=>2
[1,3,2,2,5]=>2
[1,3,2,5,2]=>1
[1,3,5,2,2]=>1
[1,5,2,2,3]=>1
[1,5,2,3,2]=>1
[1,5,3,2,2]=>2
[2,1,2,3,5]=>1
[2,1,2,5,3]=>0
[2,1,3,2,5]=>2
[2,1,3,5,2]=>1
[2,1,5,2,3]=>0
[2,1,5,3,2]=>0
[2,2,1,3,5]=>2
[2,2,1,5,3]=>1
[2,2,3,1,5]=>3
[2,2,3,5,1]=>2
[2,2,5,1,3]=>1
[2,2,5,3,1]=>1
[2,3,1,2,5]=>1
[2,3,1,5,2]=>0
[2,3,2,1,5]=>1
[2,3,2,5,1]=>0
[2,3,5,1,2]=>0
[2,3,5,2,1]=>0
[2,5,1,2,3]=>0
[2,5,1,3,2]=>0
[2,5,2,1,3]=>0
[2,5,2,3,1]=>0
[2,5,3,1,2]=>1
[2,5,3,2,1]=>1
[3,1,2,2,5]=>1
[3,1,2,5,2]=>0
[3,1,5,2,2]=>0
[3,2,1,2,5]=>2
[3,2,1,5,2]=>1
[3,2,2,1,5]=>2
[3,2,2,5,1]=>1
[3,2,5,1,2]=>1
[3,2,5,2,1]=>1
[3,5,1,2,2]=>0
[3,5,2,1,2]=>0
[3,5,2,2,1]=>0
[5,1,2,2,3]=>0
[5,1,2,3,2]=>0
[5,1,3,2,2]=>1
[5,2,1,2,3]=>1
[5,2,1,3,2]=>1
[5,2,2,1,3]=>1
[5,2,2,3,1]=>1
[5,2,3,1,2]=>2
[5,2,3,2,1]=>2
[5,3,1,2,2]=>0
[5,3,2,1,2]=>0
[5,3,2,2,1]=>0
[1,2,2,4,4]=>3
[1,2,4,2,4]=>2
[1,2,4,4,2]=>3
[1,4,2,2,4]=>1
[1,4,2,4,2]=>2
[1,4,4,2,2]=>1
[2,1,2,4,4]=>1
[2,1,4,2,4]=>0
[2,1,4,4,2]=>1
[2,2,1,4,4]=>2
[2,2,4,1,4]=>1
[2,2,4,4,1]=>2
[2,4,1,2,4]=>0
[2,4,1,4,2]=>1
[2,4,2,1,4]=>0
[2,4,2,4,1]=>1
[2,4,4,1,2]=>0
[2,4,4,2,1]=>0
[4,1,2,2,4]=>0
[4,1,2,4,2]=>1
[4,1,4,2,2]=>0
[4,2,1,2,4]=>1
[4,2,1,4,2]=>2
[4,2,2,1,4]=>1
[4,2,2,4,1]=>2
[4,2,4,1,2]=>1
[4,2,4,2,1]=>1
[4,4,1,2,2]=>0
[4,4,2,1,2]=>0
[4,4,2,2,1]=>0
[1,2,2,4,5]=>4
[1,2,2,5,4]=>2
[1,2,4,2,5]=>3
[1,2,4,5,2]=>2
[1,2,5,2,4]=>2
[1,2,5,4,2]=>3
[1,4,2,2,5]=>2
[1,4,2,5,2]=>1
[1,4,5,2,2]=>1
[1,5,2,2,4]=>1
[1,5,2,4,2]=>2
[1,5,4,2,2]=>1
[2,1,2,4,5]=>2
[2,1,2,5,4]=>0
[2,1,4,2,5]=>1
[2,1,4,5,2]=>0
[2,1,5,2,4]=>0
[2,1,5,4,2]=>1
[2,2,1,4,5]=>3
[2,2,1,5,4]=>1
[2,2,4,1,5]=>2
[2,2,4,5,1]=>1
[2,2,5,1,4]=>1
[2,2,5,4,1]=>2
[2,4,1,2,5]=>1
[2,4,1,5,2]=>0
[2,4,2,1,5]=>1
[2,4,2,5,1]=>0
[2,4,5,1,2]=>0
[2,4,5,2,1]=>0
[2,5,1,2,4]=>0
[2,5,1,4,2]=>1
[2,5,2,1,4]=>0
[2,5,2,4,1]=>1
[2,5,4,1,2]=>0
[2,5,4,2,1]=>0
[4,1,2,2,5]=>1
[4,1,2,5,2]=>0
[4,1,5,2,2]=>0
[4,2,1,2,5]=>2
[4,2,1,5,2]=>1
[4,2,2,1,5]=>2
[4,2,2,5,1]=>1
[4,2,5,1,2]=>1
[4,2,5,2,1]=>1
[4,5,1,2,2]=>0
[4,5,2,1,2]=>0
[4,5,2,2,1]=>0
[5,1,2,2,4]=>0
[5,1,2,4,2]=>1
[5,1,4,2,2]=>0
[5,2,1,2,4]=>1
[5,2,1,4,2]=>2
[5,2,2,1,4]=>1
[5,2,2,4,1]=>2
[5,2,4,1,2]=>1
[5,2,4,2,1]=>1
[5,4,1,2,2]=>0
[5,4,2,1,2]=>0
[5,4,2,2,1]=>0
[1,2,3,3,3]=>3
[1,3,2,3,3]=>1
[1,3,3,2,3]=>2
[1,3,3,3,2]=>2
[2,1,3,3,3]=>1
[2,3,1,3,3]=>0
[2,3,3,1,3]=>1
[2,3,3,3,1]=>1
[3,1,2,3,3]=>0
[3,1,3,2,3]=>1
[3,1,3,3,2]=>1
[3,2,1,3,3]=>1
[3,2,3,1,3]=>2
[3,2,3,3,1]=>2
[3,3,1,2,3]=>0
[3,3,1,3,2]=>0
[3,3,2,1,3]=>0
[3,3,2,3,1]=>0
[3,3,3,1,2]=>1
[3,3,3,2,1]=>1
[1,2,3,3,4]=>3
[1,2,3,4,3]=>4
[1,2,4,3,3]=>2
[1,3,2,3,4]=>1
[1,3,2,4,3]=>2
[1,3,3,2,4]=>2
[1,3,3,4,2]=>3
[1,3,4,2,3]=>1
[1,3,4,3,2]=>1
[1,4,2,3,3]=>1
[1,4,3,2,3]=>2
[1,4,3,3,2]=>2
[2,1,3,3,4]=>1
[2,1,3,4,3]=>2
[2,1,4,3,3]=>0
[2,3,1,3,4]=>0
[2,3,1,4,3]=>1
[2,3,3,1,4]=>1
[2,3,3,4,1]=>2
[2,3,4,1,3]=>0
[2,3,4,3,1]=>0
[2,4,1,3,3]=>0
[2,4,3,1,3]=>1
[2,4,3,3,1]=>1
[3,1,2,3,4]=>0
[3,1,2,4,3]=>1
[3,1,3,2,4]=>1
[3,1,3,4,2]=>2
[3,1,4,2,3]=>0
[3,1,4,3,2]=>0
[3,2,1,3,4]=>1
[3,2,1,4,3]=>2
[3,2,3,1,4]=>2
[3,2,3,4,1]=>3
[3,2,4,1,3]=>1
[3,2,4,3,1]=>1
[3,3,1,2,4]=>0
[3,3,1,4,2]=>1
[3,3,2,1,4]=>0
[3,3,2,4,1]=>1
[3,3,4,1,2]=>0
[3,3,4,2,1]=>0
[3,4,1,2,3]=>0
[3,4,1,3,2]=>0
[3,4,2,1,3]=>0
[3,4,2,3,1]=>0
[3,4,3,1,2]=>1
[3,4,3,2,1]=>1
[4,1,2,3,3]=>0
[4,1,3,2,3]=>1
[4,1,3,3,2]=>1
[4,2,1,3,3]=>1
[4,2,3,1,3]=>2
[4,2,3,3,1]=>2
[4,3,1,2,3]=>0
[4,3,1,3,2]=>0
[4,3,2,1,3]=>0
[4,3,2,3,1]=>0
[4,3,3,1,2]=>1
                    

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Description

The number of fixed points of a parking function.
If $(a_1,\dots,a_n)$ is a parking function, a fixed point is an index $i$ such that $a_i = i$.
It can be shown [1] that the generating function for parking functions with respect to this statistic is
$$ \frac{1}{(n+1)^2} \left((q+n)^{n+1} - (q-1)^{n+1}\right). $$

References

[1] Richard Stanley and Mei Yin, 2023, private communication.

Code

def statistic(p):
    return sum(1 for i, e in enumerate(p, 1) if i == e)

def generating_function(n):
    R. = ZZ[]
    return 1/(n+1)^2*((q+n)^(n+1) - (q-1)^(n+1))

Created

Jun 08, 2023 at 09:00 by Martin Rubey

Updated

Jun 15, 2023 at 14:41 by Martin Rubey