Identifier
Values
['A',1] => ([],1) => ([],1) => [1] => 1
['A',2] => ([(0,2),(1,2)],3) => ([(1,2)],3) => [2,1] => 2
['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] => 8
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 number of graphs with given frequency partition.
The frequency partition of a graph on $n$ vertices is the partition obtained from its degree sequence by recording and sorting the frequencies of the numbers that occur.
For example, the complete graph on $n$ vertices has frequency partition $(n)$. The path on $n$ vertices has frequency partition $(n-2,2)$, because its degree sequence is $(2,\dots,2,1,1)$. The star graph on $n$ vertices has frequency partition is $(n-1, 1)$, because its degree sequence is $(n-1,1,\dots,1)$.
There are two graphs having frequency partition $(2,1)$: the path and an edge together with an isolated vertex.
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.