- FindStat

Identifier

Mp00198: Posets —incomparability graph⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
Mp00243: Graphs —weak duplicate order⟶ Posets
St001890: Posets ⟶ ℤ

Values

([],2) => ([(0,1)],2) => ([(0,1)],2) => ([],2) => 1

([],3) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => ([],3) => 1

([(1,2)],3) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => ([],2) => 1

([(0,1),(0,2)],3) => ([(1,2)],3) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 1

([(0,2),(1,2)],3) => ([(1,2)],3) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 721 entries. <<<

search for individual values

searching the database for the individual values of this statistic

Description

The maximum magnitude of the Möbius function of a poset.
The Möbius function of a poset is the multiplicative inverse of the zeta function in the incidence algebra. The Möbius value $\mu(x, y)$ is equal to the signed sum of chains from $x$ to $y$, where odd-length chains are counted with a minus sign, so this statistic is bounded above by the total number of chains in the poset.

Map

weak duplicate order

Description

The weak duplicate order of the de-duplicate of a graph.
Let $G=(V, E)$ be a graph and let $N=\{ N_v | v\in V\}$ be the set of (distinct) neighbourhoods of $G$.
This map yields the poset obtained by ordering $N$ by reverse inclusion.

Map

connected complement

Description

The componentwise connected complement of a graph.
For a connected graph $G$, this map returns the complement of $G$ if it is connected, otherwise $G$ itself. If $G$ is not connected, the map is applied to each connected component separately.

Map

incomparability graph

Description

The incomparability graph of a poset.