Identifier
Values
([],4) => ([],4) => [1,1,1,1] => [1,1,1] => 2
([],5) => ([],5) => [1,1,1,1,1] => [1,1,1,1] => 6
([(3,4)],5) => ([(3,4)],5) => [2,1,1,1] => [1,1,1] => 2
([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,2,1] => [2,1] => 1
([],6) => ([],6) => [1,1,1,1,1,1] => [1,1,1,1,1] => 24
([(4,5)],6) => ([(4,5)],6) => [2,1,1,1,1] => [1,1,1,1] => 6
([(3,4),(3,5)],6) => ([(3,5),(4,5)],6) => [3,1,1,1] => [1,1,1] => 2
([(3,4),(4,5)],6) => ([(3,5),(4,5)],6) => [3,1,1,1] => [1,1,1] => 2
([(3,5),(4,5)],6) => ([(3,5),(4,5)],6) => [3,1,1,1] => [1,1,1] => 2
([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [3,2,1] => [2,1] => 1
([(0,5),(1,5),(2,3),(2,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [3,3] => [3] => 1
([(0,5),(1,5),(2,3),(3,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [3,3] => [3] => 1
([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [3,3] => [3] => 1
([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,2,1,1] => [2,1,1] => 3
([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [3,2,1] => [2,1] => 1
([(0,4),(0,5),(1,2),(1,3)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [3,3] => [3] => 1
([(0,5),(1,3),(1,4),(5,2)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [3,3] => [3] => 1
([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [3,2,1] => [2,1] => 1
([(0,5),(1,4),(4,2),(5,3)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [3,3] => [3] => 1
([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => [2,2,2] => [2,2] => 2
([],7) => ([],7) => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 120
([(5,6)],7) => ([(5,6)],7) => [2,1,1,1,1,1] => [1,1,1,1,1] => 24
([(4,5),(4,6)],7) => ([(4,6),(5,6)],7) => [3,1,1,1,1] => [1,1,1,1] => 6
([(3,4),(3,5),(3,6)],7) => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => [1,1,1] => 2
([(3,4),(3,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [4,1,1,1] => [1,1,1] => 2
([(3,4),(3,5),(4,6),(5,6)],7) => ([(3,5),(3,6),(4,5),(4,6)],7) => [4,1,1,1] => [1,1,1] => 2
([(4,5),(5,6)],7) => ([(4,6),(5,6)],7) => [3,1,1,1,1] => [1,1,1,1] => 6
([(3,4),(4,5),(4,6)],7) => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => [1,1,1] => 2
([(3,4),(4,6),(6,5)],7) => ([(3,6),(4,5),(5,6)],7) => [4,1,1,1] => [1,1,1] => 2
([(4,6),(5,6)],7) => ([(4,6),(5,6)],7) => [3,1,1,1,1] => [1,1,1,1] => 6
([(3,6),(4,6),(6,5)],7) => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => [1,1,1] => 2
([(3,6),(4,6),(5,6)],7) => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => [1,1,1] => 2
([(1,6),(2,6),(3,6),(4,5)],7) => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1] => [2,1] => 1
([(0,6),(1,6),(2,6),(3,4),(3,5)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1] => [2,1,1] => 3
([(1,6),(2,6),(3,4),(6,5)],7) => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1] => [2,1] => 1
([(1,6),(2,6),(3,4),(3,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1] => [3,1] => 1
([(0,6),(1,6),(2,3),(2,4),(6,5)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(0,6),(1,6),(2,3),(2,4),(2,5)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,3] => [3] => 1
([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1] => [3,1] => 1
([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(0,3),(1,6),(2,6),(3,4),(3,5)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1] => [3,1] => 1
([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [3,2,2] => [2,2] => 2
([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,3] => [3] => 1
([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,2,1,1,1] => [2,1,1,1] => 12
([(3,6),(4,5),(4,6)],7) => ([(3,6),(4,5),(5,6)],7) => [4,1,1,1] => [1,1,1] => 2
([(3,5),(3,6),(4,5),(4,6)],7) => ([(3,5),(3,6),(4,5),(4,6)],7) => [4,1,1,1] => [1,1,1] => 2
([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,2,1] => [2,1] => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,3] => [3] => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,3] => [3] => 1
([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1] => [2,1,1] => 3
([(1,6),(2,3),(2,4),(2,5)],7) => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1] => [2,1] => 1
([(0,6),(1,3),(1,4),(1,5),(6,2)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1] => [2,1] => 1
([(0,6),(1,4),(1,5),(5,3),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,2,1] => [2,1] => 1
([(0,5),(1,3),(1,4),(3,6),(4,6),(5,2)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,3] => [3] => 1
([(1,5),(1,6),(2,3),(2,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1] => [3,1] => 1
([(0,5),(0,6),(1,2),(1,3),(1,4)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(0,3),(0,4),(1,5),(1,6),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(0,2),(0,3),(1,4),(1,5),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,3] => [3] => 1
([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1] => [3,1] => 1
([(0,6),(1,4),(1,5),(6,2),(6,3)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(3,6),(4,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [4,1,1,1] => [1,1,1] => 2
([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [3,2,1,1] => [2,1,1] => 3
([(1,5),(2,6),(6,3),(6,4)],7) => ([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1] => [2,1] => 1
([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1] => [3,1] => 1
([(0,6),(1,5),(5,4),(6,2),(6,3)],7) => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [2,2,2,1] => [2,2,1] => 6
([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1] => [2,1] => 1
([(0,6),(1,5),(1,6),(2,3),(2,4)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(0,6),(1,4),(2,3),(2,6),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [3,2,2] => [2,2] => 2
([(0,6),(1,3),(1,4),(5,2),(6,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(0,6),(1,5),(2,3),(2,4),(5,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1] => [2,1] => 1
([(0,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1] => [2,1] => 1
([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [3,2,2] => [2,2] => 2
([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(3,7),(4,7),(5,7),(6,7)],8) => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => [1,1,1] => 2
([(4,6),(4,7),(5,6),(5,7)],8) => ([(4,6),(4,7),(5,6),(5,7)],8) => [4,1,1,1,1] => [1,1,1,1] => 6
([(4,7),(5,6),(5,7)],8) => ([(4,7),(5,6),(6,7)],8) => [4,1,1,1,1] => [1,1,1,1] => 6
([],8) => ([],8) => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 720
([(0,7),(1,6),(2,4),(2,7),(5,3),(6,5)],8) => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8) => [4,4] => [4] => 1
([(0,7),(1,4),(1,6),(5,3),(6,2),(7,5)],8) => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8) => [4,4] => [4] => 1
([(0,7),(1,6),(2,4),(4,7),(5,3),(6,5)],8) => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8) => [4,4] => [4] => 1
([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8) => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8) => [4,4] => [4] => 1
([(4,5),(5,7),(7,6)],8) => ([(4,7),(5,6),(6,7)],8) => [4,1,1,1,1] => [1,1,1,1] => 6
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8) => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8) => [4,2,2] => [2,2] => 2
([(4,7),(5,6)],8) => ([(4,7),(5,6)],8) => [2,2,1,1,1,1] => [2,1,1,1,1] => 60
([(0,7),(1,6),(2,5),(3,4)],8) => ([(0,7),(1,6),(2,5),(3,4)],8) => [2,2,2,2] => [2,2,2] => 16
>>> Load all 115 entries. <<<
([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8) => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8) => [4,4] => [4] => 1
([(0,5),(0,7),(1,4),(1,6),(6,2),(7,3)],8) => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8) => [4,4] => [4] => 1
([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,7),(5,7)],8) => ([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8) => [4,4] => [4] => 1
([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8) => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8) => [4,4] => [4] => 1
([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => [4,4] => [4] => 1
([(2,7),(3,7),(4,6),(5,6)],8) => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1] => [3,1,1] => 4
([(2,5),(3,4),(4,6),(5,7)],8) => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1] => [3,1,1] => 4
([(0,6),(1,6),(2,7),(3,7),(6,5),(7,4)],8) => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => [4,4] => [4] => 1
([(0,7),(1,6),(6,2),(6,3),(7,4),(7,5)],8) => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => [4,4] => [4] => 1
([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7)],8) => ([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8) => [4,4] => [4] => 1
([(2,6),(2,7),(3,4),(3,5)],8) => ([(2,7),(3,7),(4,6),(5,6)],8) => [3,3,1,1] => [3,1,1] => 4
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4)],8) => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => [4,4] => [4] => 1
([(0,6),(1,2),(1,3),(4,7),(5,7),(6,4),(6,5)],8) => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3] => [3] => 1
([(0,6),(1,6),(2,3),(2,4),(3,7),(4,7),(7,5)],8) => ([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8) => [5,3] => [3] => 1
search for individual values
searching the database for the individual values of this statistic
Description
The number of colourings of a cycle such that the multiplicities of colours are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the cyclic group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.