Identifier
Values
[1] => [.,.] => [[]] => ([(0,1)],2) => 1
[1,4,3,2] => [.,[[[.,.],.],.]] => [[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[4,3,2,1] => [[[[.,.],.],.],.] => [[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,3,5,2,4] => [.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,3,5,4,2] => [.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,5,2,4,3] => [.,[[.,[[.,.],.]],.]] => [[[[],[]],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[3,2,5,1,4] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[3,2,5,4,1] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[3,5,2,1,4] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[3,5,2,4,1] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[3,5,4,2,1] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[5,2,1,4,3] => [[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[5,2,4,1,3] => [[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[5,4,1,3,2] => [[[.,[[.,.],.]],.],.] => [[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => [[[[[]],[[]]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[1,2,5,3,6,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [[[[[]],[[]]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [[[[[]],[[]]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[1,3,4,6,5,2] => [.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[1,6,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],.]] => [[[[[],[]]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[2,1,5,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,1,5,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,5,1,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,5,1,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,5,1,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,5,3,1,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,5,3,1,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,5,3,4,1,6] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,5,3,4,6,1] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,5,3,6,1,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,5,3,6,4,1] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,5,6,1,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,5,6,3,1,4] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[2,5,6,3,4,1] => [[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[3,2,4,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[3,2,4,6,1,5] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[3,2,4,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[3,4,2,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[3,4,2,6,1,5] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[3,4,2,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[3,4,6,2,1,5] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[3,4,6,2,5,1] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[3,4,6,5,2,1] => [[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[4,1,3,2,6,5] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[4,1,3,6,2,5] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[4,1,3,6,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[4,1,6,3,2,5] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[4,1,6,3,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[4,1,6,5,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[4,6,1,3,2,5] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[4,6,1,3,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[4,6,1,5,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[4,6,5,1,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[5,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,3,1,2,6,4] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,3,1,4,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,3,1,4,6,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,3,1,6,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,3,1,6,4,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,3,4,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,3,6,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,3,6,1,4,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,3,6,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,6,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,6,3,1,4,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[6,1,4,2,3,5] => [[.,[[.,[.,.]],[.,.]]],.] => [[[[]],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[6,1,4,2,5,3] => [[.,[[.,[.,.]],[.,.]]],.] => [[[[]],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[6,1,4,5,2,3] => [[.,[[.,[.,.]],[.,.]]],.] => [[[[]],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 2
[6,2,1,3,5,4] => [[[.,.],[.,[[.,.],.]]],.] => [[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[6,2,3,1,5,4] => [[[.,.],[.,[[.,.],.]]],.] => [[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[6,2,3,5,1,4] => [[[.,.],[.,[[.,.],.]]],.] => [[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.] => [[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[6,5,1,2,4,3] => [[[.,[.,[[.,.],.]]],.],.] => [[[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
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 largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
Map
to ordered tree: left child = left brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
  • if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
  • if $x$ is the right child of $y$, $x$ becomes the last child of $y$.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.