Identifier
Values
[[[]]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[[[[]]]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[[],[[[]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 0
[[[]],[[]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[[]]],[]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 0
[[[[[]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 0
[[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[[[]]]],[]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 0
[[[],[[[]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 0
[[[[]],[[]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[[[]]],[]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 0
[[[[[[]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[],[],[[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[],[],[[[[]]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[[],[[]],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[],[[]],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[],[[]],[[[]]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[],[[[]]],[[]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[],[[[[]]]],[]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[[],[[],[[[]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[],[[[[]]],[]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[],[[[[[]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[[]],[],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[]],[],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[]],[],[[[]]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[]],[[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[]],[[[]]],[]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[]],[[],[[]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[]],[[[]],[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[[]]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[[[]]],[],[[]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[[]]],[[]],[]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[],[]],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[[[]]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[[[[]]]],[],[]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[[[],[[]]],[[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[[]],[]],[[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[],[[[]]]],[]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[[[]],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[[[]]],[]],[]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[[[[[[]]]]],[]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[[[],[],[[[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[[[],[[]],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[],[[[]]],[]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[[[],[[[[]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[[[[]],[],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[[]],[[]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[[]],[[[]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[[[]]],[],[]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[[[[[]]],[[]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[[[[]]]],[]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[[[[],[[[]]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 0
[[[[[]],[[]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[[[[]]],[]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 0
[[[[[[[]]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[],[],[],[],[[[]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[],[],[],[[]],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[],[],[],[[[]]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[],[],[],[[[[]]]]] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 0
[[],[],[[]],[],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[],[],[[]],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[],[],[[]],[[[]]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[],[],[[[]]],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[],[],[[[]]],[[]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[],[],[[[[]]]],[]] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 0
[[],[[]],[],[],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[],[[]],[],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[],[[]],[],[[[]]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[],[[]],[[]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[],[[]],[[[]]],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[],[[[]]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[],[[[]]],[],[[]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[],[[[]]],[[]],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[],[[],[]],[[[]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[],[[[]]],[[],[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[],[[[[]]]],[],[]] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 0
[[],[[[[[[]]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[[]],[],[],[],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[]],[],[],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[]],[],[],[[[]]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[]],[],[[]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[]],[],[[[]]],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[]],[[]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[[]],[[[]]],[],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[[]]],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[[[]]],[],[],[[]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[[]]],[],[[]],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[],[]],[],[[[]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[[[]]],[],[[],[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,2),(2,1)],3) => 0
>>> Load all 110 entries. <<<
[[[[]]],[[]],[],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[[],[]],[[[]]],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[[[]]],[[],[]],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[[[],[]],[[[[]]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 0
[[[[[]]]],[],[],[]] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 0
[[[[[]]]],[[],[]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 0
[[[[[[[]]]]]],[]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[[],[[[[[[[]]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[[[[[[[[]]]]]]],[]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
search for individual values
searching the database for the individual values of this statistic
Description
Number of indecomposable injective modules with projective dimension 2.
Map
antichains of maximal size
Description
The lattice of antichains of maximal size in a poset.
The set of antichains of maximal size can be ordered by setting $A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$, where $\mathop{\downarrow} A$ is the order ideal generated by $A$.
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.
Map
to poset
Description
Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.