Identifier
Values
([],1) => [1] => [1] => [1,0] => 0
([],2) => [2] => [2] => [1,1,0,0] => 0
([(0,1)],2) => [1,1] => [1,1] => [1,0,1,0] => 1
([],3) => [3] => [3] => [1,1,1,0,0,0] => 0
([(1,2)],3) => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
([(0,1),(0,2),(1,2)],3) => [2,1] => [1,2] => [1,0,1,1,0,0] => 2
([],4) => [4] => [4] => [1,1,1,1,0,0,0,0] => 0
([(2,3)],4) => [1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 1
([(1,3),(2,3)],4) => [1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 3
([(0,3),(1,2)],4) => [2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
([(1,2),(1,3),(2,3)],4) => [2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [3,1] => [1,3] => [1,0,1,1,1,0,0,0] => 3
([],5) => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
([(3,4)],5) => [1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
([(2,4),(3,4)],5) => [1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 4
([(1,4),(2,4),(3,4)],5) => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
([(1,4),(2,3)],5) => [2,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
([(2,3),(2,4),(3,4)],5) => [2,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
([(1,3),(1,4),(2,3),(2,4)],5) => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [2,1,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
([(0,1),(2,3),(2,4),(3,4)],5) => [2,1,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [3,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
([],6) => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
([(4,5)],6) => [1,5] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
([(3,5),(4,5)],6) => [1,1,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
([(2,5),(3,5),(4,5)],6) => [1,2,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
([(1,5),(2,5),(3,5),(4,5)],6) => [1,3,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
([(2,5),(3,4)],6) => [2,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
([(3,4),(3,5),(4,5)],6) => [2,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
([(0,1),(2,5),(3,5),(4,5)],6) => [1,1,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [1,1,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
([(2,4),(2,5),(3,4),(3,5)],6) => [1,2,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [2,1,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [1,1,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(0,5),(1,4),(2,3)],6) => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
([(1,2),(3,4),(3,5),(4,5)],6) => [2,1,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [1,3,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,1,2] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,2] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => [4,2] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,2] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
([(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) => [5,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
([],7) => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
([(5,6)],7) => [1,6] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
([(4,6),(5,6)],7) => [1,1,5] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
([(3,6),(4,6),(5,6)],7) => [1,2,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
([(2,6),(3,6),(4,6),(5,6)],7) => [1,3,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [1,4,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
([(3,6),(4,5)],7) => [2,5] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
([(4,5),(4,6),(5,6)],7) => [2,5] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
([(1,2),(3,6),(4,6),(5,6)],7) => [1,1,2,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [1,1,3,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [1,1,2,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [1,1,3,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
([(3,5),(3,6),(4,5),(4,6)],7) => [1,2,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [1,1,3,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [2,1,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [2,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,3,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [2,3,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
([(1,6),(2,5),(3,4)],7) => [3,4] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
([(2,3),(4,5),(4,6),(5,6)],7) => [2,1,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [2,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [2,1,2,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,1,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [2,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,4] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,3,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [2,3,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [2,1,2,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [2,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [2,1,2,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [1,4,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [1,1,3,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [2,1,2,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => [2,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [2,1,2,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [4,3] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [2,1,2,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
>>> Load all 110 entries. <<<
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,3,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
([(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) => [4,1,2] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,2] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 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) => [5,2] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
([(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) => [6,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
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
bounce path
Description
The bounce path determined by an integer composition.
Map
rotate front to back
Description
The front to back rotation of the entries of an integer composition.
Map
Laplacian multiplicities
Description
The composition of multiplicities of the Laplacian eigenvalues.
Let $\lambda_1 > \lambda_2 > \dots$ be the eigenvalues of the Laplacian matrix of a graph on $n$ vertices. Then this map returns the composition $a_1,\dots,a_k$ of $n$ where $a_i$ is the multiplicity of $\lambda_i$.