Values
=>
Cc0014;cc-rep
([],1)=>2
([],2)=>4
([(0,1)],2)=>4
([],3)=>8
([(1,2)],3)=>8
([(0,1),(0,2)],3)=>8
([(0,2),(2,1)],3)=>7
([(0,2),(1,2)],3)=>8
([],4)=>16
([(2,3)],4)=>16
([(1,2),(1,3)],4)=>16
([(0,1),(0,2),(0,3)],4)=>16
([(0,2),(0,3),(3,1)],4)=>14
([(0,1),(0,2),(1,3),(2,3)],4)=>13
([(1,2),(2,3)],4)=>14
([(0,3),(3,1),(3,2)],4)=>13
([(1,3),(2,3)],4)=>16
([(0,3),(1,3),(3,2)],4)=>13
([(0,3),(1,3),(2,3)],4)=>16
([(0,3),(1,2)],4)=>16
([(0,3),(1,2),(1,3)],4)=>16
([(0,2),(0,3),(1,2),(1,3)],4)=>16
([(0,3),(2,1),(3,2)],4)=>11
([(0,3),(1,2),(2,3)],4)=>14
([],5)=>32
([(3,4)],5)=>32
([(2,3),(2,4)],5)=>32
([(1,2),(1,3),(1,4)],5)=>32
([(0,1),(0,2),(0,3),(0,4)],5)=>32
([(0,2),(0,3),(0,4),(4,1)],5)=>28
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)=>26
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>25
([(1,3),(1,4),(4,2)],5)=>28
([(0,3),(0,4),(4,1),(4,2)],5)=>26
([(1,2),(1,3),(2,4),(3,4)],5)=>26
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>19
([(0,3),(0,4),(3,2),(4,1)],5)=>25
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>24
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>23
([(2,3),(3,4)],5)=>28
([(1,4),(4,2),(4,3)],5)=>26
([(0,4),(4,1),(4,2),(4,3)],5)=>25
([(2,4),(3,4)],5)=>32
([(1,4),(2,4),(4,3)],5)=>26
([(0,4),(1,4),(4,2),(4,3)],5)=>23
([(1,4),(2,4),(3,4)],5)=>32
([(0,4),(1,4),(2,4),(4,3)],5)=>25
([(0,4),(1,4),(2,4),(3,4)],5)=>32
([(0,4),(1,4),(2,3)],5)=>32
([(0,4),(1,3),(2,3),(2,4)],5)=>32
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>32
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>32
([(0,4),(1,4),(2,3),(4,2)],5)=>19
([(0,4),(1,3),(2,3),(3,4)],5)=>26
([(0,4),(1,4),(2,3),(2,4)],5)=>32
([(0,4),(1,4),(2,3),(3,4)],5)=>28
([(1,4),(2,3)],5)=>32
([(1,4),(2,3),(2,4)],5)=>32
([(0,4),(1,2),(1,4),(2,3)],5)=>28
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>24
([(1,3),(1,4),(2,3),(2,4)],5)=>32
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>26
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>23
([(0,4),(1,2),(1,4),(4,3)],5)=>26
([(0,4),(1,2),(1,3)],5)=>32
([(0,4),(1,2),(1,3),(1,4)],5)=>32
([(0,2),(0,4),(3,1),(4,3)],5)=>22
([(0,4),(1,2),(1,3),(3,4)],5)=>28
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>21
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>26
([(0,3),(0,4),(1,2),(1,4)],5)=>32
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>32
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>32
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>28
([(0,3),(1,2),(1,4),(3,4)],5)=>28
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>26
([(1,4),(3,2),(4,3)],5)=>22
([(0,3),(3,4),(4,1),(4,2)],5)=>19
([(1,4),(2,3),(3,4)],5)=>28
([(0,4),(1,2),(2,4),(4,3)],5)=>21
([(0,3),(1,4),(4,2)],5)=>28
([(0,4),(3,2),(4,1),(4,3)],5)=>21
([(0,4),(1,2),(2,3),(2,4)],5)=>26
([(0,4),(2,3),(3,1),(4,2)],5)=>16
([(0,3),(1,2),(2,4),(3,4)],5)=>25
([(0,4),(1,2),(2,3),(3,4)],5)=>22
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>19
([],6)=>64
([(4,5)],6)=>64
([(3,4),(3,5)],6)=>64
([(2,3),(2,4),(2,5)],6)=>64
([(1,2),(1,3),(1,4),(1,5)],6)=>64
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)=>64
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)=>56
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)=>52
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)=>50
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>49
([(1,3),(1,4),(1,5),(5,2)],6)=>56
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)=>52
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>52
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>50
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>35
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)=>47
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)=>45
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>44
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>43
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)=>46
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>37
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)=>38
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)=>50
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)=>48
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)=>46
([(2,3),(2,4),(4,5)],6)=>56
([(1,4),(1,5),(5,2),(5,3)],6)=>52
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)=>50
([(2,3),(2,4),(3,5),(4,5)],6)=>52
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>38
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)=>31
([(1,4),(1,5),(4,3),(5,2)],6)=>50
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>48
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>46
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)=>35
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>31
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)=>36
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)=>47
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)=>46
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)=>45
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)=>44
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>43
([(3,4),(4,5)],6)=>56
([(2,3),(3,4),(3,5)],6)=>52
([(1,5),(5,2),(5,3),(5,4)],6)=>50
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)=>49
([(2,3),(3,5),(5,4)],6)=>44
([(1,4),(4,5),(5,2),(5,3)],6)=>38
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)=>35
([(3,5),(4,5)],6)=>64
([(2,5),(3,5),(5,4)],6)=>52
([(1,5),(2,5),(5,3),(5,4)],6)=>46
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)=>43
([(2,5),(3,5),(4,5)],6)=>64
([(1,5),(2,5),(3,5),(5,4)],6)=>50
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)=>43
([(1,5),(2,5),(3,5),(4,5)],6)=>64
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)=>49
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>64
([(0,5),(1,5),(2,5),(3,4)],6)=>64
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)=>35
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)=>50
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)=>64
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>56
([(1,5),(2,5),(3,4)],6)=>64
([(1,5),(2,4),(3,4),(3,5)],6)=>64
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)=>52
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)=>45
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>64
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)=>52
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)=>44
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>64
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>50
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>43
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>50
([(1,5),(2,5),(3,4),(5,3)],6)=>38
([(1,5),(2,4),(3,4),(4,5)],6)=>52
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>37
([(0,5),(1,5),(2,3),(5,4)],6)=>52
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)=>35
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)=>46
([(1,5),(2,5),(3,4),(3,5)],6)=>64
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)=>50
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)=>56
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)=>46
([(0,5),(1,5),(2,3),(2,4)],6)=>64
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)=>31
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)=>52
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>46
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)=>64
([(0,5),(1,2),(1,4),(3,5),(4,3)],6)=>44
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)=>38
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>35
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)=>56
([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)=>42
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>37
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>52
([(1,5),(2,5),(3,4),(4,5)],6)=>56
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>41
([(0,5),(1,5),(2,3),(3,4)],6)=>56
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>26
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)=>47
([(0,5),(1,4),(3,5),(4,2),(4,3)],6)=>42
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>37
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)=>52
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>44
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>38
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>35
([(0,5),(1,5),(2,4),(3,4)],6)=>64
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)=>64
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>64
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>64
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>64
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>64
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)=>38
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>31
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>52
([(2,5),(3,4)],6)=>64
([(2,5),(3,4),(3,5)],6)=>64
([(1,5),(2,3),(2,5),(3,4)],6)=>56
([(0,5),(1,4),(1,5),(4,2),(4,3)],6)=>52
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)=>44
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)=>40
([(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>48
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)=>33
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)=>46
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)=>42
([(2,4),(2,5),(3,4),(3,5)],6)=>64
([(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>52
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)=>46
([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>46
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)=>43
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)=>40
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)=>37
([(0,4),(0,5),(1,4),(1,5),(2,3)],6)=>64
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)=>38
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)=>31
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)=>35
([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6)=>52
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>46
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)=>64
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6)=>52
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>64
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>56
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6)=>56
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>52
([(1,5),(2,3),(2,5),(5,4)],6)=>52
([(0,5),(1,2),(1,5),(5,3),(5,4)],6)=>46
([(1,5),(2,3),(2,4)],6)=>64
([(1,5),(2,3),(2,4),(2,5)],6)=>64
([(0,5),(1,3),(1,4),(1,5),(4,2)],6)=>56
([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>48
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6)=>52
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>46
([(0,5),(1,2),(1,3),(1,5),(5,4)],6)=>52
([(0,5),(1,2),(1,3),(1,4)],6)=>64
([(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>64
([(0,2),(0,3),(0,5),(4,1),(5,4)],6)=>44
([(0,5),(1,2),(1,3),(1,4),(4,5)],6)=>56
([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)=>42
([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>52
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>41
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>50
([(0,4),(1,2),(1,3),(1,5),(4,5)],6)=>56
([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6)=>52
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>50
([(1,3),(1,5),(4,2),(5,4)],6)=>44
([(0,3),(0,4),(4,5),(5,1),(5,2)],6)=>38
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>40
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>39
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>33
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)=>39
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)=>38
([(1,5),(2,3),(2,4),(4,5)],6)=>56
([(0,5),(1,2),(1,3),(3,5),(5,4)],6)=>42
([(1,3),(1,4),(2,5),(3,5),(4,2)],6)=>42
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>29
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>52
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>37
([(0,5),(1,3),(1,4),(3,5),(4,2)],6)=>50
([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6)=>48
([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>46
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6)=>40
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)=>40
([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>48
([(0,4),(1,3),(1,5),(5,2)],6)=>56
([(0,3),(0,5),(4,2),(5,1),(5,4)],6)=>42
([(0,5),(1,3),(1,4),(4,2),(4,5)],6)=>52
([(0,4),(1,2),(1,3),(3,5),(4,5)],6)=>50
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>31
([(0,4),(1,2),(1,3),(2,5),(3,5)],6)=>52
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>47
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>26
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>38
([(1,4),(1,5),(2,3),(2,5)],6)=>64
([(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>64
([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)=>52
([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6)=>46
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>64
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)=>52
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)=>46
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>43
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6)=>56
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)=>48
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>44
([(0,4),(0,5),(1,3),(1,5),(5,2)],6)=>52
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>56
([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6)=>46
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)=>42
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)=>38
([(0,3),(0,5),(1,4),(1,5),(4,2)],6)=>56
([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6)=>48
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6)=>52
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)=>44
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6)=>50
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6)=>45
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)=>44
([(0,4),(0,5),(1,2),(1,3)],6)=>64
([(0,4),(0,5),(1,2),(1,3),(1,5)],6)=>64
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>64
([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)=>56
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)=>52
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6)=>64
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>64
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>64
([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)=>56
([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6)=>56
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6)=>52
([(0,4),(0,5),(1,2),(1,3),(3,5)],6)=>56
([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6)=>52
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)=>35
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)=>36
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6)=>52
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>50
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6)=>48
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>46
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)=>49
([(1,4),(2,3),(2,5),(4,5)],6)=>56
([(0,4),(1,3),(1,5),(4,5),(5,2)],6)=>42
([(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>52
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)=>40
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>35
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)=>49
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)=>39
([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6)=>46
([(0,5),(1,3),(1,4),(5,2)],6)=>56
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>32
([(0,5),(4,2),(4,3),(5,1),(5,4)],6)=>37
([(0,4),(1,3),(1,5),(4,2),(4,5)],6)=>52
([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6)=>50
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)=>42
([(2,5),(3,4),(4,5)],6)=>56
([(1,5),(2,3),(3,5),(5,4)],6)=>42
([(0,5),(1,2),(2,5),(5,3),(5,4)],6)=>35
([(1,3),(2,4),(4,5)],6)=>56
([(1,5),(4,3),(5,2),(5,4)],6)=>42
([(1,5),(2,3),(3,4),(3,5)],6)=>52
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)=>40
([(0,4),(1,5),(5,2),(5,3)],6)=>52
([(0,5),(4,3),(5,1),(5,2),(5,4)],6)=>41
([(0,5),(1,4),(4,2),(4,3),(4,5)],6)=>50
([(1,5),(3,4),(4,2),(5,3)],6)=>32
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)=>26
([(1,4),(2,3),(3,5),(4,5)],6)=>50
([(0,4),(1,3),(3,5),(4,5),(5,2)],6)=>35
([(0,5),(1,4),(4,2),(5,3)],6)=>49
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)=>31
([(0,3),(1,4),(3,5),(4,2),(4,5)],6)=>46
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)=>43
([(1,5),(2,3),(3,4),(4,5)],6)=>44
([(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>38
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>26
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>31
([(0,5),(1,4),(2,3)],6)=>64
([(0,5),(1,3),(2,4),(2,5)],6)=>64
([(0,5),(1,4),(2,3),(2,4),(2,5)],6)=>64
([(0,5),(1,4),(1,5),(3,2),(4,3)],6)=>44
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>39
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>56
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)=>36
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>48
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)=>38
([(0,5),(1,4),(2,3),(2,4),(4,5)],6)=>52
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)=>64
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>64
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>64
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)=>64
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6)=>64
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>64
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>64
([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6)=>52
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>64
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>56
([(0,5),(1,4),(1,5),(2,3),(2,5)],6)=>64
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>56
([(0,4),(1,4),(1,5),(2,3),(3,5)],6)=>56
([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>52
([(0,4),(1,3),(1,5),(2,5),(4,2)],6)=>44
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)=>38
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)=>31
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)=>33
([(0,5),(1,4),(2,3),(2,5),(4,5)],6)=>56
([(0,5),(1,3),(4,2),(5,4)],6)=>44
([(0,5),(3,2),(4,1),(5,3),(5,4)],6)=>35
([(0,5),(1,4),(3,2),(4,3),(4,5)],6)=>42
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)=>36
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>29
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)=>38
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>22
([(0,5),(1,3),(2,4),(4,5)],6)=>56
([(0,5),(1,4),(2,3),(3,4),(3,5)],6)=>52
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>29
([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>42
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>32
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>26
([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>40
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>29
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>50
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Description
The number of interval-closed sets of a poset.
For a poset $P$ and a subset $I$ of $P$, we say that $I$ is an interval-closed set if for all $x, y \in I$ such that $x \leq y$, then $z \in I$ if $x \leq z \leq y$.
There is a bijection between interval-closed sets of a poset $P$ and pairs of disjoint antichains $(A, B)$ of $P$ such that any element in $B$ is in the order ideal $\Delta(A)$ generated by $A$. (Proposition 2.5 of [1]).
For a poset $P$ and a subset $I$ of $P$, we say that $I$ is an interval-closed set if for all $x, y \in I$ such that $x \leq y$, then $z \in I$ if $x \leq z \leq y$.
There is a bijection between interval-closed sets of a poset $P$ and pairs of disjoint antichains $(A, B)$ of $P$ such that any element in $B$ is in the order ideal $\Delta(A)$ generated by $A$. (Proposition 2.5 of [1]).
References
[1] Elder, J., Lafrenière, N., McNicholas, E., Striker, J., Welch, A. Toggling, rowmotion, and homomesy on interval-closed sets arXiv:2307.08520
Code
def statistic(x):
ICS_count = 0
for A in x.antichains_iterator():
I = x.order_ideal(A)
Q = x.subposet(set(I).difference(A))
ICS_count += Q.antichains().cardinality()
return ICS_count
Created
Jul 28, 2023 at 18:44 by Nadia Lafreniere
Updated
Jan 19, 2024 at 18:31 by Nadia Lafreniere
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