Values
=>
Cc0014;cc-rep-0
Cc0029;cc-rep
([],1)=>([(0,1)],2)=>0
([],2)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
([(0,1)],2)=>([(0,2),(2,1)],3)=>1
([(1,2)],3)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
([(0,1),(0,2)],3)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>2
([(0,2),(2,1)],3)=>([(0,3),(2,1),(3,2)],4)=>2
([(0,2),(1,2)],3)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
([(0,2),(0,3),(3,1)],4)=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>2
([(0,1),(0,2),(1,3),(2,3)],4)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>2
([(0,3),(3,1),(3,2)],4)=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>3
([(0,3),(1,3),(3,2)],4)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>3
([(0,2),(0,3),(1,2),(1,3)],4)=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>4
([(0,3),(2,1),(3,2)],4)=>([(0,4),(2,3),(3,1),(4,2)],5)=>3
([(0,3),(1,2),(2,3)],4)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>3
([(0,4),(1,4),(2,3),(4,2)],5)=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>4
([(0,3),(3,4),(4,1),(4,2)],5)=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>4
([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>3
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>5
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Description
The number of doubly irreducible elements of a lattice.
An element $d$ of a lattice $L$ is doubly irreducible if it is both join and meet irreducible. That means, $d$ is neither the least nor the greatest element of $L$ and if $d=x\vee y$ or $d=x\wedge y$, then $d\in\{x,y\}$ for all $x,y\in L$.
In a finite lattice, the doubly irreducible elements are those which cover and are covered by a unique element.
An element $d$ of a lattice $L$ is doubly irreducible if it is both join and meet irreducible. That means, $d$ is neither the least nor the greatest element of $L$ and if $d=x\vee y$ or $d=x\wedge y$, then $d\in\{x,y\}$ for all $x,y\in L$.
In a finite lattice, the doubly irreducible elements are those which cover and are covered by a unique element.
Map
order ideals
Description
The lattice of order ideals of a poset.
An order ideal $\mathcal I$ in a poset $P$ is a downward closed set, i.e., $a \in \mathcal I$ and $b \leq a$ implies $b \in \mathcal I$. This map sends a poset to the lattice of all order ideals sorted by inclusion with meet being intersection and join being union.
An order ideal $\mathcal I$ in a poset $P$ is a downward closed set, i.e., $a \in \mathcal I$ and $b \leq a$ implies $b \in \mathcal I$. This map sends a poset to the lattice of all order ideals sorted by inclusion with meet being intersection and join being union.
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