Identifier
Values
['A',1] => ([],1) => 0
['A',2] => ([(0,2),(1,2)],3) => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => 1
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 1
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 2
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Description
The jump number of the poset.
A jump in a linear extension $e_1, \dots, e_n$ of a poset $P$ is a pair $(e_i, e_{i+1})$ so that $e_{i+1}$ does not cover $e_i$ in $P$. The jump number of a poset is the minimal number of jumps in 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.