Identifier
Values
[[],[]] => ([(0,2),(1,2)],3) => [2] => 0
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => [3,3] => 0
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => [3] => 0
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => [3] => 0
[[[],[]]] => ([(0,3),(1,3),(3,2)],4) => [2] => 0
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4,4,4] => 0
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4,4,4] => 0
[[],[[],[]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => [8] => 0
[[],[[[]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4] => 0
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4,4,4] => 0
[[[]],[[]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => [4,2] => 0
[[[],[]],[]] => ([(0,4),(1,3),(2,3),(3,4)],5) => [8] => 0
[[[[]]],[]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4] => 0
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(4,3)],5) => [3,3] => 0
[[[],[[]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [3] => 0
[[[[]],[]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [3] => 0
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => [2] => 0
[[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => [5,5] => 0
[[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [5] => 0
[[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [5,5] => 0
[[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [5,5] => 0
[[[[],[]]],[]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => [5,5] => 0
[[[[[]]]],[]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [5] => 0
[[[],[],[[]]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => [4,4,4] => 0
[[[],[[]],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => [4,4,4] => 0
[[[],[[],[]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => [8] => 0
[[[],[[[]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => [4] => 0
[[[[]],[],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => [4,4,4] => 0
[[[[]],[[]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => 0
[[[[],[]],[]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => [8] => 0
[[[[[]]],[]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => [4] => 0
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => [3,3] => 0
[[[[],[[]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [3] => 0
[[[[[]],[]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [3] => 0
[[[[[],[]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [2] => 0
[[],[[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [12] => 0
[[],[[[[[]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => [6] => 0
[[[[[],[]]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [12] => 0
[[[[[[]]]]],[]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => [6] => 0
[[[],[[[],[]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => [5,5] => 0
[[[],[[[[]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [5] => 0
[[[[]],[[[]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [5,5] => 0
[[[[[]]],[[]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [5,5] => 0
[[[[[],[]]],[]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => [5,5] => 0
[[[[[[]]]],[]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [5] => 0
[[[[],[],[[]]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => [4,4,4] => 0
[[[[],[[]],[]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => [4,4,4] => 0
[[[[],[[],[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => [8] => 0
[[[[],[[[]]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => [4] => 0
[[[[[]],[],[]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => [4,4,4] => 0
[[[[[]],[[]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => [4,2] => 0
[[[[[],[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => [8] => 0
[[[[[[]]],[]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => [4] => 0
[[[[[],[],[]]]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => [3,3] => 0
[[[[[],[[]]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [3] => 0
[[[[[[]],[]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [3] => 0
[[[[[[],[]]]]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => [2] => 0
search for individual values
searching the database for the individual values of this statistic
Description
The constant term of the character polynomial of an integer partition.
The definition of the character polynomial can be found in [1]. Indeed, this constant term is $0$ for partitions $\lambda \neq 1^n$ and $1$ for $\lambda = 1^n$.
Map
to poset
Description
Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.
Map
promotion cycle type
Description
The cycle type of promotion on the linear extensions of a poset.