Identifier
Values
['A',2] => ([(0,2),(1,2)],3) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 2
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Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
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
Dedekind-MacNeille completion
Description
Return the smallest lattice containing the poset.