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
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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
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
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
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.