Identifier
Values
[1] => [1,0] => [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[2] => [1,0,1,0] => [3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 1
[1,1] => [1,1,0,0] => [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 1
[2,1] => [1,0,1,1,0,0] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 3
[] => [] => [1] => ([(0,1)],2) => -1
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Description
The Möbius invariant of a lattice.
The Möbius invariant of a lattice $L$ is the value of the Möbius function applied to least and greatest element, that is $\mu(L)=\mu_L(\hat{0},\hat{1})$, where $\hat{0}$ is the least element of $L$ and $\hat{1}$ is the greatest element of $L$.
For the definition of the Möbius function, see St000914The sum of the values of the Möbius function of a poset..
Map
lattice of intervals
Description
The lattice of intervals of a permutation.
An interval of a permutation $\pi$ is a possibly empty interval of values that appear in consecutive positions of $\pi$. The lattice of intervals of $\pi$ has as elements the intervals of $\pi$, ordered by set inclusion.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.