Identifier
Values
['A',1] => ([],1) => ([],1) => 1
['A',2] => ([(0,2),(1,2)],3) => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 13
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Description
The number of tolerances of a finite lattice.
Let $L$ be a lattice. A tolerance $\tau$ is a reflexive and symmetric relation on $L$ which is compatible with meet and join. Equivalently, a tolerance of $L$ is the image of a congruence by a surjective lattice homomorphism onto $L$.
The number of tolerances of a chain of $n$ elements is the Catalan number $\frac{1}{n+1}\binom{2n}{n}$, see [2].
Let $L$ be a lattice. A tolerance $\tau$ is a reflexive and symmetric relation on $L$ which is compatible with meet and join. Equivalently, a tolerance of $L$ is the image of a congruence by a surjective lattice homomorphism onto $L$.
The number of tolerances of a chain of $n$ elements is the Catalan number $\frac{1}{n+1}\binom{2n}{n}$, see [2].
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.
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.
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