Identifier
Values
[1,0] => [1] => ([],1) => 0
[1,0,1,0] => [2,1] => ([(0,1)],2) => 0
[1,1,0,0] => [1,2] => ([(0,1)],2) => 0
[1,0,1,0,1,0] => [3,2,1] => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,0] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[1,1,0,0,1,0] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[1,1,0,1,0,0] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[1,1,1,0,0,0] => [1,2,3] => ([(0,2),(2,1)],3) => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 0
[1,0,1,0,1,1,0,0] => [3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[1,0,1,1,1,0,0,0] => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[1,1,0,0,1,0,1,0] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[1,1,0,0,1,1,0,0] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2
[1,1,0,1,0,1,0,0] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[1,1,1,0,0,0,1,0] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[1,1,1,0,1,0,0,0] => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[1,1,1,1,0,0,0,0] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 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 number of simple modules with projective dimension two in the incidence algebra of the poset.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
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.