Identifier
Values
([(0,2),(1,2)],3) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 2
([(0,1),(0,2),(1,2)],3) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(1,3),(2,3)],4) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 2
([(0,3),(1,3),(2,3)],4) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(0,3),(1,2)],4) => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 2
([(0,3),(1,2),(2,3)],4) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(1,2),(1,3),(2,3)],4) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(0,3),(1,2),(1,3),(2,3)],4) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(0,2),(0,3),(1,2),(1,3)],4) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(2,4),(3,4)],5) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 2
([(1,4),(2,4),(3,4)],5) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(0,4),(1,4),(2,4),(3,4)],5) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(1,4),(2,3)],5) => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 2
([(1,4),(2,3),(3,4)],5) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(2,3),(2,4),(3,4)],5) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(0,4),(1,4),(2,3),(3,4)],5) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(1,4),(2,3),(2,4),(3,4)],5) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(1,3),(1,4),(2,3),(2,4)],5) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(0,4),(1,3),(2,3),(2,4)],5) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(0,1),(2,3),(2,4),(3,4)],5) => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(3,5),(4,5)],6) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 2
([(2,5),(3,5),(4,5)],6) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(1,5),(2,5),(3,5),(4,5)],6) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(2,5),(3,4)],6) => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 2
([(2,5),(3,4),(4,5)],6) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(3,4),(3,5),(4,5)],6) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(1,5),(2,5),(3,4),(4,5)],6) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(0,1),(2,5),(3,5),(4,5)],6) => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(2,5),(3,4),(3,5),(4,5)],6) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(2,4),(2,5),(3,4),(3,5)],6) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(0,5),(1,5),(2,4),(3,4)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 3
([(0,5),(1,4),(2,3)],6) => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 3
([(1,5),(2,4),(3,4),(3,5)],6) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(0,1),(2,5),(3,4),(4,5)],6) => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(1,2),(3,4),(3,5),(4,5)],6) => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 3
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
([(4,6),(5,6)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 2
([(3,6),(4,6),(5,6)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(2,6),(3,6),(4,6),(5,6)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(3,6),(4,5)],7) => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 2
([(3,6),(4,5),(5,6)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(4,5),(4,6),(5,6)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
([(2,6),(3,6),(4,5),(5,6)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(1,2),(3,6),(4,6),(5,6)],7) => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(3,6),(4,5),(4,6),(5,6)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 3
([(3,5),(3,6),(4,5),(4,6)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(1,6),(2,6),(3,5),(4,5)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 3
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 2
([(1,6),(2,5),(3,4)],7) => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 3
([(2,6),(3,5),(4,5),(4,6)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 3
([(1,2),(3,6),(4,5),(5,6)],7) => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,3),(1,2),(4,6),(5,6)],7) => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2
([(2,3),(4,5),(4,6),(5,6)],7) => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 3
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 3
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 3
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 2
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 2
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 3
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 3
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 3
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 3
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 3
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 3
search for individual values
searching the database for the individual values of this statistic
Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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
to edge-partition of connected components
Description
Sends a graph to the partition recording the number of edges in its connected components.