Identifier
Values
['A',1] => ([],1) => ([],1) => 0
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 0
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => 1
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
['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) => 2
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 minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph.
A graph is a disjoint union of paths if and only if in any linear ordering of its vertices, there are no three vertices $a < b < c$ such that $(a,c)$ is an edge. This statistic is the minimal number of occurrences of this pattern, in the set of all linear orderings of the vertices.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected 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.