Values
=>
Cc0029;cc-rep
([],1)=>1
([(0,1)],2)=>-1
([(0,2),(2,1)],3)=>0
([(0,1),(0,2),(1,3),(2,3)],4)=>1
([(0,3),(2,1),(3,2)],4)=>0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>0
([(0,4),(2,3),(3,1),(4,2)],5)=>0
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>0
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>3
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>0
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>0
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>0
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>0
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>0
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>0
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>0
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>4
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)=>3
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>0
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)=>0
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)=>0
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)=>0
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>1
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>0
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>0
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>0
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>0
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)=>2
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>0
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)=>1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>0
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)=>0
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)=>0
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)=>1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>0
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>0
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)=>0
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)=>0
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)=>0
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)=>2
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)=>1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>0
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>0
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>0
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)=>0
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>0
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>0
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>0
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>0
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>0
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>0
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>1
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>0
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)=>1
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>0
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>1
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>0
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>0
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>0
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>0
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>0
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>0
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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..
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..
Code
def statistic(L):
return L.moebius_function(L.bottom(), L.top())
Created
Oct 01, 2020 at 09:22 by Henri Mühle
Updated
Feb 08, 2021 at 23:23 by Martin Rubey
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