Identifier
Values
['A',1] => ([],1) => ([],1) => [1] => 0
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => [3] => 3
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => [4] => 6
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [6] => 15
['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) => [6] => 15
['B',3] => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9) => ([(0,8),(1,7),(2,6),(3,6),(3,8),(4,7),(4,8),(5,6),(5,7),(5,8)],9) => [9] => 36
['C',3] => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9) => ([(0,8),(1,7),(2,6),(3,6),(3,8),(4,7),(4,8),(5,6),(5,7),(5,8)],9) => [9] => 36
['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) => ([(0,8),(1,7),(2,5),(2,6),(3,7),(3,9),(4,8),(4,9),(5,7),(5,9),(6,8),(6,9)],10) => [10] => 45
['B',4] => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16) => ([(0,15),(1,11),(2,10),(3,13),(3,15),(4,14),(4,15),(5,10),(5,13),(6,11),(6,14),(7,8),(7,9),(7,12),(8,10),(8,13),(9,11),(9,14),(12,13),(12,14),(12,15)],16) => [16] => 120
['C',4] => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16) => ([(0,15),(1,11),(2,10),(3,13),(3,15),(4,14),(4,15),(5,10),(5,13),(6,11),(6,14),(7,8),(7,9),(7,12),(8,10),(8,13),(9,11),(9,14),(12,13),(12,14),(12,15)],16) => [16] => 120
['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) => ([(0,11),(1,10),(2,9),(3,8),(4,8),(4,9),(4,10),(5,8),(5,9),(5,11),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11)],12) => [12] => 66
['A',5] => ([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15) => ([(0,11),(1,10),(2,8),(2,9),(3,10),(3,13),(4,11),(4,14),(5,13),(5,14),(6,8),(6,10),(6,13),(7,9),(7,11),(7,14),(8,12),(9,12),(12,13),(12,14)],15) => [15] => 105
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
click to show known generating functions       
Description
The Gini index of an integer partition.
As discussed in [1], this statistic is equal to St000567The sum of the products of all pairs of parts. applied to the conjugate 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.
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.