- FindStat

Identifier

St000327: Posets ⟶ ℤ

Values

=>
                            Cc0014;cc-rep
                            
                            
                            

                        ([],2)=>0
([(0,1)],2)=>1
([],3)=>0
([(1,2)],3)=>1
([(0,1),(0,2)],3)=>2
([(0,2),(2,1)],3)=>2
([(0,2),(1,2)],3)=>2
([],4)=>0
([(2,3)],4)=>1
([(1,2),(1,3)],4)=>2
([(0,1),(0,2),(0,3)],4)=>3
([(0,2),(0,3),(3,1)],4)=>3
([(0,1),(0,2),(1,3),(2,3)],4)=>4
([(1,2),(2,3)],4)=>2
([(0,3),(3,1),(3,2)],4)=>3
([(1,3),(2,3)],4)=>2
([(0,3),(1,3),(3,2)],4)=>3
([(0,3),(1,3),(2,3)],4)=>3
([(0,3),(1,2)],4)=>2
([(0,3),(1,2),(1,3)],4)=>3
([(0,2),(0,3),(1,2),(1,3)],4)=>4
([(0,3),(2,1),(3,2)],4)=>3
([(0,3),(1,2),(2,3)],4)=>3
([],5)=>0
([(3,4)],5)=>1
([(2,3),(2,4)],5)=>2
([(1,2),(1,3),(1,4)],5)=>3
([(0,1),(0,2),(0,3),(0,4)],5)=>4
([(0,2),(0,3),(0,4),(4,1)],5)=>4
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)=>5
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>6
([(1,3),(1,4),(4,2)],5)=>3
([(0,3),(0,4),(4,1),(4,2)],5)=>4
([(1,2),(1,3),(2,4),(3,4)],5)=>4
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
([(0,3),(0,4),(3,2),(4,1)],5)=>4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>6
([(2,3),(3,4)],5)=>2
([(1,4),(4,2),(4,3)],5)=>3
([(0,4),(4,1),(4,2),(4,3)],5)=>4
([(2,4),(3,4)],5)=>2
([(1,4),(2,4),(4,3)],5)=>3
([(0,4),(1,4),(4,2),(4,3)],5)=>4
([(1,4),(2,4),(3,4)],5)=>3
([(0,4),(1,4),(2,4),(4,3)],5)=>4
([(0,4),(1,4),(2,4),(3,4)],5)=>4
([(0,4),(1,4),(2,3)],5)=>3
([(0,4),(1,3),(2,3),(2,4)],5)=>4
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>5
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>6
([(0,4),(1,4),(2,3),(4,2)],5)=>4
([(0,4),(1,3),(2,3),(3,4)],5)=>4
([(0,4),(1,4),(2,3),(2,4)],5)=>4
([(0,4),(1,4),(2,3),(3,4)],5)=>4
([(1,4),(2,3)],5)=>2
([(1,4),(2,3),(2,4)],5)=>3
([(0,4),(1,2),(1,4),(2,3)],5)=>4
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>5
([(1,3),(1,4),(2,3),(2,4)],5)=>4
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>5
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>6
([(0,4),(1,2),(1,4),(4,3)],5)=>4
([(0,4),(1,2),(1,3)],5)=>3
([(0,4),(1,2),(1,3),(1,4)],5)=>4
([(0,2),(0,4),(3,1),(4,3)],5)=>4
([(0,4),(1,2),(1,3),(3,4)],5)=>4
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>5
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>5
([(0,3),(0,4),(1,2),(1,4)],5)=>4
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>5
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>6
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>5
([(0,3),(1,2),(1,4),(3,4)],5)=>4
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>5
([(1,4),(3,2),(4,3)],5)=>3
([(0,3),(3,4),(4,1),(4,2)],5)=>4
([(1,4),(2,3),(3,4)],5)=>3
([(0,4),(1,2),(2,4),(4,3)],5)=>4
([(0,3),(1,4),(4,2)],5)=>3
([(0,4),(3,2),(4,1),(4,3)],5)=>4
([(0,4),(1,2),(2,3),(2,4)],5)=>4
([(0,4),(2,3),(3,1),(4,2)],5)=>4
([(0,3),(1,2),(2,4),(3,4)],5)=>4
([(0,4),(1,2),(2,3),(3,4)],5)=>4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
                    

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The number of cover relations in a poset.
Equivalently, this is also the number of edges in the Hasse diagram [1].

References

[1] wikipedia:Hasse_diagram

Code

def statistic(P):
    return len(P.cover_relations())

Created

Dec 13, 2015 at 01:36 by Daniel Shira

Updated

Dec 13, 2015 at 07:44 by Christian Stump