Identifier
Values
=>
Cc0029;cc-rep
[1]=>([(0,1)],2)=>0 [1,2]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2 [2,1]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2 [1,2,3]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>2 [1,3,2]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>3 [2,1,3]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>3 [2,3,1]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>3 [3,1,2]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>3 [3,2,1]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>2 [2,4,1,3]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>4 [3,1,4,2]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>4 [2,4,1,5,3]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5 [2,5,3,1,4]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5 [3,1,5,2,4]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5 [3,5,1,4,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5 [4,1,3,5,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5 [4,2,5,1,3]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
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searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
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.
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.