Identifier
Values
[1] => [1] => ([],1) => ([(0,1)],2) => 2
[1,2] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2
[2,1] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2
[1,2,3] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
[1,3,2] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
[2,1,3] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
[2,3,1] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2
[1,2,3,4] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,2,4,3] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,3,2,4] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,3,4,2] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,1,3,4] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,1,4,3] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,3,1,4] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,3,4,1] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,2,3,4,5] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,3,5,4] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,4,3,5] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,4,5,3] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,3,2,4,5] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,3,2,5,4] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,3,4,2,5] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,3,4,5,2] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,3,4,5] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,3,5,4] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,4,3,5] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,4,5,3] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,1,4,5] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,1,5,4] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,4,1,5] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,4,5,1] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,1,3,5,6,4] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,1,4,3,5,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,1,4,3,6,5] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,1,4,5,3,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,1,4,5,6,3] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,1,4,5,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,1,4,6,5] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,1,5,4,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,1,5,6,4] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,1,5,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,1,6,5] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,5,1,6] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,5,6,1] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,3,4,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,3,4,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,3,4,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,3,5,4,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,3,5,4,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,3,5,6,4,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,3,5,6,7,4] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,4,3,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,4,3,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,4,3,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,4,3,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,4,5,3,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,4,5,3,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,4,5,6,3,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,4,5,6,7,3] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,2,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,2,4,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,2,4,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,2,4,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,2,5,4,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,2,5,4,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,2,5,6,4,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,2,5,6,7,4] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,4,2,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,4,2,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,4,2,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,4,2,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,4,5,2,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,4,5,2,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,4,5,6,2,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,3,4,5,6,7,2] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,3,4,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,3,4,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,3,4,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,3,5,4,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,3,5,4,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
>>> Load all 128 entries. <<<
[2,1,3,5,6,4,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,3,5,6,7,4] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,4,3,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,4,3,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,4,3,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,4,3,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,4,5,3,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,4,5,3,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,4,5,6,3,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,4,5,6,7,3] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,1,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,1,4,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,1,4,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,1,4,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,1,5,4,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,1,5,4,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,1,5,6,4,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,1,5,6,7,4] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,1,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,1,5,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,1,6,5,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,1,6,7,5] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,5,1,6,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,5,1,7,6] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,5,6,1,7] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[] => [] => ([],0) => ([],1) => 1
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
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cone
Description
The cone of a graph.
The cone of a graph is obtained by joining a new vertex to all the vertices of the graph. The added vertex is called a universal vertex or a dominating vertex.
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
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.