Identifier
Values
[1] => ([],1) => ([],1) => ([],1) => 1
[1,2] => ([(0,1)],2) => ([],2) => ([],2) => 2
[2,1] => ([(0,1)],2) => ([],2) => ([],2) => 2
[1,2,3] => ([(0,2),(2,1)],3) => ([],3) => ([],3) => 3
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => ([(2,3)],4) => 4
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => ([(2,3)],4) => 4
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => ([(2,3)],4) => 4
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => ([(2,3)],4) => 4
[3,2,1] => ([(0,2),(2,1)],3) => ([],3) => ([],3) => 3
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([],4) => ([],4) => 4
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 6
[1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 7
[1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 7
[1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 7
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 6
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 6
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 6
[2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 7
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 6
[2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 7
[3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 7
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 6
[3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 7
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 6
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 6
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 6
[4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 7
[4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 7
[4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 7
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 6
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => ([],4) => ([],4) => 4
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => ([],5) => 5
[5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => ([],5) => 5
[1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => ([],6) => 6
[6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => ([],6) => 6
[1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => ([],7) => 7
[7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => ([],7) => 7
[8,7,6,5,4,3,2,1] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([],8) => ([],8) => 8
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 Ramsey number of a graph.
This is the smallest integer $n$ such that every two-colouring of the edges of the complete graph $K_n$ contains a (not necessarily induced) monochromatic copy of the given graph. [1]
Thus, the Ramsey number of the complete graph $K_n$ is the ordinary Ramsey number $R(n,n)$. Very few of these numbers are known, in particular, it is only known that $43\leq R(5,5)\leq 48$. [2,3,4,5]
This is the smallest integer $n$ such that every two-colouring of the edges of the complete graph $K_n$ contains a (not necessarily induced) monochromatic copy of the given graph. [1]
Thus, the Ramsey number of the complete graph $K_n$ is the ordinary Ramsey number $R(n,n)$. Very few of these numbers are known, in particular, it is only known that $43\leq R(5,5)\leq 48$. [2,3,4,5]
Map
connected complement
Description
The componentwise connected complement of a graph.
For a connected graph $G$, this map returns the complement of $G$ if it is connected, otherwise $G$ itself. If $G$ is not connected, the map is applied to each connected component separately.
For a connected graph $G$, this map returns the complement of $G$ if it is connected, otherwise $G$ itself. If $G$ is not connected, the map is applied to each connected component separately.
Map
pattern poset
Description
The pattern poset of a permutation.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
Map
incomparability graph
Description
The incomparability graph of a poset.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!