Identifier
Values
[1,0] => [1] => [1] => ([],1) => -1
[1,0,1,0] => [2,1] => [2,1] => ([(0,1)],2) => -1
[1,1,0,0] => [1,2] => [1,2] => ([(0,1)],2) => -1
[1,0,1,0,1,0] => [2,3,1] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => -1
[1,0,1,1,0,0] => [2,1,3] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => -1
[1,1,0,0,1,0] => [1,3,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => -1
[1,1,0,1,0,0] => [3,1,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => -1
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3) => -1
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -1
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -1
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => -1
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -1
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -1
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -1
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -1
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => -1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => -1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => -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
Description
The trace of the Coxeter matrix of the incidence algebra of a poset.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.