Identifier
-
Mp00163:
Signed permutations
—permutation⟶
Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤ
Values
=>
Cc0014;cc-rep
[1,2,3]=>[1,2,3]=>([(0,2),(2,1)],3)=>3
[1,2,-3]=>[1,2,3]=>([(0,2),(2,1)],3)=>3
[1,-2,3]=>[1,2,3]=>([(0,2),(2,1)],3)=>3
[1,-2,-3]=>[1,2,3]=>([(0,2),(2,1)],3)=>3
[-1,2,3]=>[1,2,3]=>([(0,2),(2,1)],3)=>3
[-1,2,-3]=>[1,2,3]=>([(0,2),(2,1)],3)=>3
[-1,-2,3]=>[1,2,3]=>([(0,2),(2,1)],3)=>3
[-1,-2,-3]=>[1,2,3]=>([(0,2),(2,1)],3)=>3
[1,2,3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[1,2,3,-4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[1,2,-3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[1,2,-3,-4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[1,-2,3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[1,-2,3,-4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[1,-2,-3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[1,-2,-3,-4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[-1,2,3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[-1,2,3,-4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[-1,2,-3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[-1,2,-3,-4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[-1,-2,3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[-1,-2,3,-4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[-1,-2,-3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[-1,-2,-3,-4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>4
[1,3,2,4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[1,3,2,-4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[1,3,-2,4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[1,3,-2,-4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[1,-3,2,4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[1,-3,2,-4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[1,-3,-2,4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[1,-3,-2,-4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[-1,3,2,4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[-1,3,2,-4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[-1,3,-2,4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[-1,3,-2,-4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[-1,-3,2,4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[-1,-3,2,-4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[-1,-3,-2,4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[-1,-3,-2,-4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[1,2,3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,2,3,4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,2,3,-4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,2,3,-4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,2,-3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,2,-3,4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,2,-3,-4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,2,-3,-4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,-2,3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,-2,3,4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,-2,3,-4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,-2,3,-4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,-2,-3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,-2,-3,4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,-2,-3,-4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,-2,-3,-4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,2,3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,2,3,4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,2,3,-4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,2,3,-4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,2,-3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,2,-3,4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,2,-3,-4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,2,-3,-4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,-2,3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,-2,3,4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,-2,3,-4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,-2,3,-4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,-2,-3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,-2,-3,4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,-2,-3,-4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[-1,-2,-3,-4,-5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>5
[1,2,4,3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,2,4,3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,2,4,-3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,2,4,-3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,2,-4,3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,2,-4,3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,2,-4,-3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,2,-4,-3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,-2,4,3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,-2,4,3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,-2,4,-3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,-2,4,-3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,-2,-4,3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,-2,-4,3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,-2,-4,-3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,-2,-4,-3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,2,4,3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,2,4,3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,2,4,-3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,2,4,-3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,2,-4,3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,2,-4,3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,2,-4,-3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,2,-4,-3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,-2,4,3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,-2,4,3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,-2,4,-3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,-2,4,-3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,-2,-4,3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,-2,-4,3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,-2,-4,-3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[-1,-2,-4,-3,-5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,3,2,4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,3,2,4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,3,2,-4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,3,2,-4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,3,-2,4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,3,-2,4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,3,-2,-4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,3,-2,-4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,-3,2,4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,-3,2,4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,-3,2,-4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,-3,2,-4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,-3,-2,4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,-3,-2,4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,-3,-2,-4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,-3,-2,-4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,3,2,4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,3,2,4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,3,2,-4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,3,2,-4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,3,-2,4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,3,-2,4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,3,-2,-4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,3,-2,-4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,-3,2,4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,-3,2,4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,-3,2,-4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,-3,2,-4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,-3,-2,4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,-3,-2,4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,-3,-2,-4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[-1,-3,-2,-4,-5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,3,4,2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,3,4,2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,3,4,-2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,3,4,-2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,3,-4,2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,3,-4,2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,3,-4,-2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,3,-4,-2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-3,4,2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-3,4,2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-3,4,-2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-3,4,-2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-3,-4,2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-3,-4,2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-3,-4,-2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-3,-4,-2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,3,4,2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,3,4,2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,3,4,-2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,3,4,-2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,3,-4,2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,3,-4,2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,3,-4,-2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,3,-4,-2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-3,4,2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-3,4,2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-3,4,-2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-3,4,-2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-3,-4,2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-3,-4,2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-3,-4,-2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-3,-4,-2,-5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,4,2,3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,4,2,3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,4,2,-3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,4,2,-3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,4,-2,3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,4,-2,3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,4,-2,-3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,4,-2,-3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-4,2,3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-4,2,3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-4,2,-3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-4,2,-3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-4,-2,3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-4,-2,3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-4,-2,-3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,-4,-2,-3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,4,2,3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,4,2,3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,4,2,-3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,4,2,-3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,4,-2,3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,4,-2,3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,4,-2,-3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,4,-2,-3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-4,2,3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-4,2,3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-4,2,-3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-4,2,-3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-4,-2,3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-4,-2,3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-4,-2,-3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[-1,-4,-2,-3,-5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>4
[1,4,3,2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,4,3,2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,4,3,-2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,4,3,-2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,4,-3,2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,4,-3,2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,4,-3,-2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,4,-3,-2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,-4,3,2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,-4,3,2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,-4,3,-2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,-4,3,-2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,-4,-3,2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,-4,-3,2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,-4,-3,-2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,-4,-3,-2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,4,3,2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,4,3,2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,4,3,-2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,4,3,-2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,4,-3,2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,4,-3,2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,4,-3,-2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,4,-3,-2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,-4,3,2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,-4,3,2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,-4,3,-2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,-4,3,-2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,-4,-3,2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,-4,-3,2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,-4,-3,-2,5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[-1,-4,-3,-2,-5]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>6
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>5
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>5
[1,4,5,2,3,6]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>4
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>4
[1,-5,-4,2,3,6]=>[1,5,4,2,3,6]=>([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>1
[1,-4,2,3,5,6]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>5
[1,-5,2,3,4,6]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>4
[1,-3,5,2,4,6]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>6
[1,-3,2,4,5,6]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[1,4,-3,2,5,6]=>[1,4,3,2,5,6]=>([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>2
[1,4,5,-3,2,6]=>[1,4,5,3,2,6]=>([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>1
[1,-5,2,-4,3,6]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>2
[1,2,-4,3,5,6]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[1,2,5,-4,3,6]=>[1,2,5,4,3,6]=>([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>2
[1,2,3,-5,4,6]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[1,2,-4,-5,3,6]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>5
[1,4,-3,-5,2,6]=>[1,4,3,5,2,6]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>2
[1,-3,-4,2,5,6]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>5
[1,-3,5,-4,2,6]=>[1,3,5,4,2,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>2
[1,-3,-4,-5,2,6]=>[1,3,4,5,2,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>4
[1,3,-5,-4,2,6]=>[1,3,5,4,2,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>2
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Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
permutation
Description
The permutation obtained by forgetting the colours.
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