Processing math: 100%

Identifier
Values
{{1,2}} => {{1,2}} => [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
{{1},{2}} => {{1},{2}} => [1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
{{1,2,3}} => {{1,2,3}} => [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 2
{{1,2},{3}} => {{1,2},{3}} => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 2
{{1,3},{2}} => {{1,3},{2}} => [3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 2
{{1},{2,3}} => {{1},{2,3}} => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 2
{{1},{2},{3}} => {{1},{2},{3}} => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 2
{{1,5},{2,3},{4}} => {{1,3},{2,5},{4}} => [3,5,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,5},{2},{3,4}} => {{1,4},{2},{3,5}} => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
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 global dimension of the incidence algebra of the lattice over the rational numbers.
Map
inverse Wachs-White-rho
Description
The inverse of a transformation of set partitions due to Wachs and White.
Return the set partition of {1,...,n} corresponding to the set of arcs, interpreted as a rook placement, applying Wachs and White's bijection ρ−1.
Note that our index convention differs from the convention in [1]: regarding the rook board as a lower-right triangular grid, we refer with (i,j) to the cell in the i-th column from the right and the j-th row from the top.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
lattice of intervals
Description
The lattice of intervals of a permutation.
An interval of a permutation π is a possibly empty interval of values that appear in consecutive positions of π. The lattice of intervals of π has as elements the intervals of π, ordered by set inclusion.