Identifier
Values
['A',1] => ([],1) => ([],1) => [1] => 1
['A',2] => ([(0,2),(1,2)],3) => ([(1,2)],3) => [2,1] => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => [2,1,1] => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6) => [2,1,1,1,1] => 2
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [5,1] => 1
['B',3] => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9) => ([(2,7),(3,5),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9) => [7,1,1] => 2
['C',3] => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9) => ([(2,7),(3,5),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9) => [7,1,1] => 2
['A',4] => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10) => ([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10) => [9,1] => 1
['D',4] => ([(0,10),(1,9),(2,8),(3,8),(3,9),(3,10),(5,11),(6,11),(7,11),(8,5),(8,6),(9,5),(9,7),(10,6),(10,7),(11,4)],12) => ([(2,9),(2,10),(2,11),(3,4),(3,5),(3,8),(3,11),(4,5),(4,7),(4,10),(5,6),(5,9),(6,7),(6,8),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(9,11),(10,11)],12) => [10,1,1] => 2
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Description
The number of different multiplicities of parts of an integer partition.
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
Map
to root poset
Description
The root poset of a finite Cartan type.
This is the poset on the set of positive roots of its root system where $\alpha \prec \beta$ if $\beta - \alpha$ is a simple root.
Map
incomparability graph
Description
The incomparability graph of a poset.