Identifier
Values
{{1}} => [1] => [1] => ([],1) => -1
{{1,2}} => [2,1] => [2,1] => ([(0,1)],2) => -1
{{1},{2}} => [1,2] => [1,2] => ([(0,1)],2) => -1
{{1,2,3}} => [2,3,1] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => -1
{{1,2},{3}} => [2,1,3] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => -1
{{1,3},{2}} => [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3) => -1
{{1},{2,3}} => [1,3,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => -1
{{1},{2},{3}} => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3) => -1
{{1,2,3,4}} => [2,3,4,1] => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
{{1,2,3},{4}} => [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
{{1,2,4},{3}} => [2,4,3,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -1
{{1,2},{3},{4}} => [2,1,3,4] => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
{{1,3,4},{2}} => [3,2,4,1] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -1
{{1,3},{2},{4}} => [3,2,1,4] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
{{1,4},{2,3}} => [4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => -1
{{1},{2,3,4}} => [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},{2,3},{4}} => [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
{{1,4},{2},{3}} => [4,2,3,1] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => -1
{{1},{2,4},{3}} => [1,4,3,2] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
{{1},{2},{3,4}} => [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},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => -1
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => -1
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => -1
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => -1
{{1},{2},{3},{4},{5},{6}} => [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
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
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.