Identifier
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [1,2] => [1,2] => [1,2] => 0
[1,1,0,0] => [2,1] => [2,1] => [2,1] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => [3,1,2] => [3,1,2] => 2
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [2,1,3] => 1
[1,1,0,1,0,0] => [2,3,1] => [2,3,1] => [2,3,1] => 1
[1,1,1,0,0,0] => [3,1,2] => [1,3,2] => [1,3,2] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [4,1,2,3] => [4,1,2,3] => 3
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,4,1,2] => [3,4,1,2] => 2
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [1,4,2,3] => [1,4,2,3] => 2
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,3,4,1] => [2,3,4,1] => 1
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [4,2,1,3] => [4,2,1,3] => 2
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [1,3,4,2] => [1,3,4,2] => 1
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [3,1,4,2] => [3,1,4,2] => 2
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [1,2,4,3] => [1,2,4,3] => 1
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 number of preferred parking spots in a parking function less than the index of the car.
Let $(a_1,\dots,a_n)$ be a parking function. Then this statistic returns the number of indices $1\leq i\leq n$ such that $a_i < i$.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
Map
parking function
Description
Interpret the permutation as a parking function.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.