Identifier
Values
[1] => [1,0] => [2,1] => ([],2) => 0
[3] => [1,0,1,0,1,0] => [4,1,2,3] => ([(1,2),(2,3)],4) => 0
[2,1] => [1,0,1,1,0,0] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4) => 0
[4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 0
[3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => ([(0,4),(1,2),(2,3),(2,4)],5) => 1
[2,2] => [1,1,1,0,0,0] => [2,3,4,1] => ([(1,2),(2,3)],4) => 0
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 0
[5] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 0
[3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5) => 1
[2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(1,4)],5) => 1
[1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 0
[2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5) => 0
[4,4] => [1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 0
[2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6) => 0
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => 0
[] => [] => [1] => ([],1) => 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
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$