Identifier
Values
[1] => ([],1) => ([],1) => 1
[1,2] => ([(0,1)],2) => ([],2) => 1
[2,1] => ([(0,1)],2) => ([],2) => 1
[1,2,3] => ([(0,2),(2,1)],3) => ([],3) => 1
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 2
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 2
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 2
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 2
[3,2,1] => ([(0,2),(2,1)],3) => ([],3) => 1
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 1
[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
[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) => 3
[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) => 3
[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) => 3
[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
[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
[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
[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) => 3
[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
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8) => ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[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) => 3
[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) => 3
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8) => ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[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
[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) => 3
[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
[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
[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
[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) => 3
[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) => 3
[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) => 3
[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
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 1
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 1
[1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8) => 2
[1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8) => 2
[2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8) => 2
[2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8) => 2
[4,3,2,1,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8) => 2
[4,5,3,2,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8) => 2
[5,1,2,3,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8) => 2
[5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8) => 2
[5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 1
[1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 1
[6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 1
[1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 1
[7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 1
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 chromatic number of a graph.
The minimal number of colors needed to color the vertices of the graph such that no two vertices which share an edge have the same color.
The minimal number of colors needed to color the vertices of the graph such that no two vertices which share an edge have the same color.
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!