Identifier
Values
['A',1] => ([],1) => ([],1) => [1] => 0
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => [3] => 0
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => [4] => 0
['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] => 0
['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] => 0
['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] => 0
['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] => 0
['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] => 0
['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] => 0
['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] => 0
['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] => 0
['F',4] => ([(0,18),(1,19),(2,18),(2,22),(3,19),(3,22),(4,6),(6,5),(7,11),(8,16),(9,17),(10,13),(10,14),(11,4),(12,23),(13,8),(13,23),(14,9),(14,23),(15,11),(16,15),(17,7),(17,15),(18,20),(19,21),(20,12),(20,13),(21,12),(21,14),(22,10),(22,20),(22,21),(23,16),(23,17)],24) => ([(0,15),(1,16),(2,9),(3,15),(3,22),(4,16),(4,22),(5,17),(5,19),(6,12),(6,17),(7,9),(7,12),(8,13),(8,18),(10,18),(10,19),(10,22),(11,20),(11,21),(11,23),(12,14),(13,14),(13,23),(14,17),(15,20),(16,21),(17,23),(18,20),(18,23),(19,21),(19,23),(20,22),(21,22)],24) => [24] => 0
['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] => 0
['D',5] => ([(0,13),(1,16),(2,15),(3,13),(3,17),(4,15),(4,16),(4,17),(6,10),(7,19),(8,19),(9,18),(10,5),(11,7),(11,18),(12,8),(12,18),(13,14),(14,7),(14,8),(15,9),(15,11),(16,9),(16,12),(17,11),(17,12),(17,14),(18,6),(18,19),(19,10)],20) => ([(0,17),(1,16),(2,11),(3,10),(4,10),(4,18),(5,11),(5,19),(6,16),(6,17),(6,18),(7,16),(7,17),(7,19),(8,12),(8,13),(8,14),(9,12),(9,13),(9,15),(10,12),(11,13),(12,18),(13,19),(14,16),(14,18),(14,19),(15,17),(15,18),(15,19)],20) => [20] => 0
['A',6] => ([(0,14),(1,13),(2,18),(2,20),(3,19),(3,20),(4,13),(4,18),(5,14),(5,19),(7,9),(8,10),(9,11),(10,12),(11,6),(12,6),(13,7),(14,8),(15,9),(15,17),(16,10),(16,17),(17,11),(17,12),(18,7),(18,15),(19,8),(19,16),(20,15),(20,16)],21) => ([(0,14),(1,13),(2,18),(2,20),(3,19),(3,20),(4,11),(4,12),(5,13),(5,18),(6,14),(6,19),(7,9),(7,13),(7,18),(8,10),(8,14),(8,19),(9,11),(9,15),(10,12),(10,16),(11,17),(12,17),(15,17),(15,18),(15,20),(16,17),(16,19),(16,20)],21) => [21] => 0
['D',6] => ([(0,24),(1,23),(2,20),(3,22),(3,26),(4,20),(4,22),(5,23),(5,24),(5,26),(7,12),(8,19),(9,27),(10,29),(11,29),(12,6),(13,16),(13,27),(14,17),(14,27),(15,21),(16,10),(16,28),(17,11),(17,28),(18,12),(19,7),(19,18),(20,15),(21,10),(21,11),(22,15),(22,25),(23,9),(23,13),(24,9),(24,14),(25,16),(25,17),(25,21),(26,13),(26,14),(26,25),(27,8),(27,28),(28,19),(28,29),(29,18)],30) => ([(0,25),(1,24),(2,15),(3,14),(4,22),(4,28),(5,23),(5,29),(6,14),(6,22),(7,15),(7,23),(8,18),(8,20),(8,21),(9,19),(9,20),(9,21),(10,24),(10,25),(10,28),(11,24),(11,25),(11,29),(12,14),(12,20),(12,22),(13,15),(13,21),(13,23),(16,18),(16,24),(16,28),(16,29),(17,19),(17,25),(17,28),(17,29),(18,26),(18,27),(19,26),(19,27),(20,26),(21,27),(22,26),(23,27),(26,28),(27,29)],30) => [30] => 0
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 floored half-sum of the multiplicities of a partition.
This statistic is equidistributed with St000143The largest repeated part of a partition. and St000149The number of cells of the partition whose leg is zero and arm is odd., see [1].
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.
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.