Identifier
Values
[1,0] => [.,.] => [[]] => ([(0,1)],2) => 2
[1,0,1,0] => [.,[.,.]] => [[],[]] => ([(0,2),(1,2)],3) => 3
[1,1,0,0] => [[.,.],.] => [[[]]] => ([(0,2),(1,2)],3) => 3
[1,0,1,0,1,0] => [.,[.,[.,.]]] => [[],[],[]] => ([(0,3),(1,3),(2,3)],4) => 4
[1,1,0,0,1,0] => [[.,[.,.]],.] => [[[],[]]] => ([(0,3),(1,3),(2,3)],4) => 4
[1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => [[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 5
[1,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],.] => [[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 5
[1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => [[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 6
[1,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],.] => [[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 6
[1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 7
[1,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => [[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 7
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 Laplacian eigenvalue of a graph if it is integral.
This statistic is undefined if the largest Laplacian eigenvalue of the graph is not integral.
Various results are collected in Section 3.9 of [1]
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.
Map
to ordered tree: right child = right brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
  • if $x$ is the right child of $y$, $x$ becomes the right brother of $y$,
  • if $x$ is the left child of $y$, $x$ becomes the first child of $y$.
Map
logarithmic height to pruning number
Description
Francon's map from Dyck paths to binary trees.
This bijection sends the logarithmic height of the Dyck path, St000920The logarithmic height of a Dyck path., to the pruning number of the binary tree, St000396The register function (or Horton-Strahler number) of a binary tree.. The implementation is a literal translation of Knuth's [2].