Identifier
Values
['A',2] => ([(0,2),(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 16
['B',3] => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9) => 42
['C',3] => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9) => 42
['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) => 768
['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) => 24024
['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) => 24024
['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) => 2400
['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) => 2311020
['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) => 292864
['B',5] => ([(0,18),(1,17),(2,18),(2,24),(3,23),(3,24),(4,17),(4,23),(6,15),(7,16),(8,9),(9,5),(10,12),(11,13),(12,11),(13,14),(14,9),(15,7),(15,21),(16,8),(16,14),(17,10),(18,6),(18,19),(19,15),(19,22),(20,12),(20,22),(21,13),(21,16),(22,11),(22,21),(23,10),(23,20),(24,19),(24,20)],25) => 701149020
['C',5] => ([(0,18),(1,17),(2,18),(2,24),(3,23),(3,24),(4,17),(4,23),(6,15),(7,16),(8,9),(9,5),(10,12),(11,13),(12,11),(13,14),(14,9),(15,7),(15,21),(16,8),(16,14),(17,10),(18,6),(18,19),(19,15),(19,22),(20,12),(20,22),(21,13),(21,16),(22,11),(22,21),(23,10),(23,20),(24,19),(24,20)],25) => 701149020
['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) => 14082624
['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) => 1100742656
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Description
The number of linear extensions of a poset.
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.