Identifier
Values
[1] => [1,0] => [1] => ([],1) => 0
[2] => [1,0,1,0] => [2,1] => ([(0,1)],2) => 1
[1,1] => [1,1,0,0] => [1,2] => ([],2) => 0
[2,1] => [1,0,1,1,0,0] => [2,1,3] => ([(1,2)],3) => 1
[2,2] => [1,1,1,0,0,0] => [1,2,3] => ([],3) => 0
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[5] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[3,2] => [1,0,1,1,1,0,0,0] => [2,1,3,4] => ([(2,3)],4) => 1
[5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => ([],4) => 0
[2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 2
[3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => ([(3,4)],5) => 1
[3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 2
[6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 2
[2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 2
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => ([],5) => 0
[3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 2
[5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => ([(4,5)],6) => 1
[3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 2
[5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 3
[4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => ([],6) => 0
[4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => ([(5,6)],7) => 1
[3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => ([],7) => 0
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
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.