Identifier
Values
[1] => [1] => [1] => ([],1) => 0
[1,2] => [2,1] => [1,2] => ([(0,1)],2) => 0
[2,1] => [1,2] => [1,2] => ([(0,1)],2) => 0
[1,2,3] => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3) => 0
[1,3,2] => [3,2,1] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[2,1,3] => [1,3,2] => [1,2,3] => ([(0,2),(2,1)],3) => 0
[2,3,1] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3) => 0
[3,1,2] => [3,1,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[3,2,1] => [2,1,3] => [1,2,3] => ([(0,2),(2,1)],3) => 0
[1,2,3,4] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 0
[2,1,3,4] => [1,3,4,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 0
[2,3,1,4] => [1,2,4,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 0
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 0
[2,4,3,1] => [1,3,2,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 0
[3,2,1,4] => [2,1,4,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 0
[3,2,4,1] => [2,1,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 0
[4,2,3,1] => [2,3,1,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 0
[1,2,3,4,5] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,1,3,4,5] => [1,3,4,5,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,3,1,4,5] => [1,2,4,5,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,3,4,1,5] => [1,2,3,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,3,5,4,1] => [1,2,4,3,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,4,3,1,5] => [1,3,2,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,4,3,5,1] => [1,3,2,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,5,3,4,1] => [1,3,4,2,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,2,1,4,5] => [2,1,4,5,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,2,4,1,5] => [2,1,3,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,2,4,5,1] => [2,1,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,2,5,4,1] => [2,1,4,3,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,2,3,1,5] => [2,3,1,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,2,3,5,1] => [2,3,1,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,2,3,4,1] => [2,3,4,1,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,2,3,4,5,6] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,1,3,4,5,6] => [1,3,4,5,6,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,1,4,5,6] => [1,2,4,5,6,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,4,1,5,6] => [1,2,3,5,6,4] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,4,5,1,6] => [1,2,3,4,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,4,6,5,1] => [1,2,3,5,4,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,5,4,1,6] => [1,2,4,3,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,5,4,6,1] => [1,2,4,3,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,6,4,5,1] => [1,2,4,5,3,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,3,1,5,6] => [1,3,2,5,6,4] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,3,5,1,6] => [1,3,2,4,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,3,5,6,1] => [1,3,2,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,3,6,5,1] => [1,3,2,5,4,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,5,3,4,1,6] => [1,3,4,2,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,5,3,4,6,1] => [1,3,4,2,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,6,3,4,5,1] => [1,3,4,5,2,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,1,4,5,6] => [2,1,4,5,6,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,4,1,5,6] => [2,1,3,5,6,4] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,4,5,1,6] => [2,1,3,4,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,4,5,6,1] => [2,1,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,4,6,5,1] => [2,1,3,5,4,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,5,4,1,6] => [2,1,4,3,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,5,4,6,1] => [2,1,4,3,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,6,4,5,1] => [2,1,4,5,3,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,2,3,1,5,6] => [2,3,1,5,6,4] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,2,3,5,1,6] => [2,3,1,4,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,2,3,5,6,1] => [2,3,1,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,2,3,6,5,1] => [2,3,1,5,4,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,3,4,1,6] => [2,3,4,1,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,3,4,6,1] => [2,3,4,1,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,2,3,4,5,1] => [2,3,4,5,1,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
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
Description
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
Map
pattern poset
Description
The pattern poset of a permutation.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.