Identifier
Values
['A',1] => ([],1) => ([],1) => 0
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => 3
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 3
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 number of edges that can be added without increasing the maximal degree of a graph.
This statistic is (except for the degenerate case of two vertices) maximized by the star-graph on $n$ vertices, which has maximal degree $n-1$ and therefore has statistic $\binom{n-1}{2}$.
This statistic is (except for the degenerate case of two vertices) maximized by the star-graph on $n$ vertices, which has maximal degree $n-1$ and therefore has statistic $\binom{n-1}{2}$.
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.
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
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
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!