Identifier
-
Mp00209:
Permutations
—pattern poset⟶
Posets
St000845: Posets ⟶ ℤ
Values
=>
Cc0014;cc-rep
[1]=>([],1)=>0
[1,2]=>([(0,1)],2)=>1
[2,1]=>([(0,1)],2)=>1
[1,2,3]=>([(0,2),(2,1)],3)=>1
[1,3,2]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[2,1,3]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[2,3,1]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[3,1,2]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[3,2,1]=>([(0,2),(2,1)],3)=>1
[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>1
[1,2,4,3]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[1,3,2,4]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>3
[1,3,4,2]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>3
[1,4,2,3]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>3
[1,4,3,2]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[2,1,3,4]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[2,1,4,3]=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>2
[2,3,1,4]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>3
[2,3,4,1]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[2,4,3,1]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>3
[3,1,2,4]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>3
[3,2,1,4]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[3,2,4,1]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>3
[3,4,1,2]=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>2
[3,4,2,1]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[4,1,2,3]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[4,1,3,2]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>3
[4,2,1,3]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>3
[4,2,3,1]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>3
[4,3,1,2]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[4,3,2,1]=>([(0,3),(2,1),(3,2)],4)=>1
[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[5,4,3,2,1]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[6,5,4,3,2,1]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
[7,6,5,4,3,2,1]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
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Description
The maximal number of elements covered by an element in a poset.
Map
pattern poset
Description
The pattern poset of a permutation.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
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