Identifier
Values
([],1) => [1] => [1,0] => [1,0] => 0
([],2) => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
([(0,1)],2) => [2] => [1,0,1,0] => [1,1,0,0] => 0
([],3) => [1,1,1] => [1,1,0,1,0,0] => [1,1,0,1,0,0] => 2
([(1,2)],3) => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
([(0,1),(0,2),(1,2)],3) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
([],4) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 3
([(2,3)],4) => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2
([(1,2),(1,3),(2,3)],4) => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
([],5) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
([(3,4)],5) => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
([(2,3),(2,4),(3,4)],5) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
([],6) => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
([(4,5)],6) => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
([(3,4),(3,5),(4,5)],6) => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
([],7) => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
([(5,6)],7) => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 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 number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Map
Lalanne-Kreweras involution
Description
The Lalanne-Kreweras involution on Dyck paths.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
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
clique sizes
Description
The integer partition of the sizes of the maximal cliques of a graph.