Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001709
Mapping
St001709: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 3
([],2)
 => 9
([(0,1)],2)
 => 6
([],3)
 => 27
([(1,2)],3)
 => 18
([(0,1),(0,2)],3)
 => 14
([(0,2),(2,1)],3)
 => 10
([(0,2),(1,2)],3)
 => 14
([],4)
 => 81
([(2,3)],4)
 => 54
([(1,2),(1,3)],4)
 => 42
([(0,1),(0,2),(0,3)],4)
 => 36
([(0,2),(0,3),(3,1)],4)
 => 25
([(0,1),(0,2),(1,3),(2,3)],4)
 => 20
([(1,2),(2,3)],4)
 => 30
([(0,3),(3,1),(3,2)],4)
 => 20
([(1,3),(2,3)],4)
 => 42
([(0,3),(1,3),(3,2)],4)
 => 20
([(0,3),(1,3),(2,3)],4)
 => 36
([(0,3),(1,2)],4)
 => 36
([(0,3),(1,2),(1,3)],4)
 => 31
([(0,2),(0,3),(1,2),(1,3)],4)
 => 26
([(0,3),(2,1),(3,2)],4)
 => 15
([(0,3),(1,2),(2,3)],4)
 => 25
([],5)
 => 243
([(3,4)],5)
 => 162
([(2,3),(2,4)],5)
 => 126
([(1,2),(1,3),(1,4)],5)
 => 108
([(0,1),(0,2),(0,3),(0,4)],5)
 => 98
([(0,2),(0,3),(0,4),(4,1)],5)
 => 67
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 53
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 46
([(1,3),(1,4),(4,2)],5)
 => 75
([(0,3),(0,4),(4,1),(4,2)],5)
 => 53
([(1,2),(1,3),(2,4),(3,4)],5)
 => 60
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 27
([(0,3),(0,4),(3,2),(4,1)],5)
 => 46
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 40
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 34
([(2,3),(3,4)],5)
 => 90
([(1,4),(4,2),(4,3)],5)
 => 60
([(0,4),(4,1),(4,2),(4,3)],5)
 => 46
([(2,4),(3,4)],5)
 => 126
([(1,4),(2,4),(4,3)],5)
 => 60
([(0,4),(1,4),(4,2),(4,3)],5)
 => 34
([(1,4),(2,4),(3,4)],5)
 => 108
([(0,4),(1,4),(2,4),(4,3)],5)
 => 46
([(0,4),(1,4),(2,4),(3,4)],5)
 => 98
([(0,4),(1,4),(2,3)],5)
 => 84
([(0,4),(1,3),(2,3),(2,4)],5)
 => 70
Description
The number of homomorphisms to the three element chain of a poset. This is the evaluation of the order polynomial at $3$.
Matching statistic: St001762
Mapping
Mp00195: Posets —order ideals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001762: Graphs ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 9%
Values
([],1)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 4 = 3 + 1
([],2)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 10 = 9 + 1
([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 7 = 6 + 1
([],3)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)
 => ? = 27 + 1
([(1,2)],3)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => 19 = 18 + 1
([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 15 = 14 + 1
([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 11 = 10 + 1
([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 15 = 14 + 1
([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ([(0,12),(0,13),(0,14),(0,15),(1,5),(1,9),(1,10),(1,11),(2,5),(2,7),(2,8),(2,11),(3,5),(3,6),(3,8),(3,10),(4,5),(4,6),(4,7),(4,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14)],16)
 => ? ∊ {30,31,36,36,36,42,42,54,81} + 1
([(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12)
 => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12)
 => ([(0,4),(0,5),(0,9),(1,2),(1,3),(1,9),(2,6),(2,11),(3,6),(3,10),(4,7),(4,10),(5,7),(5,11),(6,8),(7,8),(8,10),(8,11),(9,10),(9,11)],12)
 => ? ∊ {30,31,36,36,36,42,42,54,81} + 1
([(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
 => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
 => ([(0,1),(0,9),(1,8),(2,3),(2,4),(2,5),(3,6),(3,7),(4,7),(4,8),(5,6),(5,8),(6,9),(7,9),(8,9)],10)
 => ? ∊ {30,31,36,36,36,42,42,54,81} + 1
([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,8),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9)
 => ? ∊ {30,31,36,36,36,42,42,54,81} + 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => 26 = 25 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 21 = 20 + 1
([(1,2),(2,3)],4)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? ∊ {30,31,36,36,36,42,42,54,81} + 1
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => 21 = 20 + 1
([(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
 => ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
 => ([(0,1),(0,9),(1,8),(2,3),(2,4),(2,5),(3,6),(3,7),(4,7),(4,8),(5,6),(5,8),(6,9),(7,9),(8,9)],10)
 => ? ∊ {30,31,36,36,36,42,42,54,81} + 1
([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => 21 = 20 + 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,8),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9)
 => ? ∊ {30,31,36,36,36,42,42,54,81} + 1
([(0,3),(1,2)],4)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
 => ? ∊ {30,31,36,36,36,42,42,54,81} + 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? ∊ {30,31,36,36,36,42,42,54,81} + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
 => 27 = 26 + 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 16 = 15 + 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => 26 = 25 + 1
([],5)
 => ?
 => ?
 => ?
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(3,4)],5)
 => ?
 => ?
 => ?
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)
 => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)
 => ([(0,2),(0,3),(0,19),(1,2),(1,3),(1,18),(2,17),(3,16),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,10),(5,11),(6,12),(6,13),(7,14),(7,15),(8,13),(8,15),(8,16),(9,12),(9,14),(9,16),(10,12),(10,14),(10,17),(11,13),(11,15),(11,17),(12,18),(13,18),(14,19),(15,19),(16,18),(16,19),(17,18),(17,19)],20)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(1,2),(1,3),(1,4)],5)
 => ([(0,1),(0,2),(1,12),(2,3),(2,4),(2,5),(2,12),(3,8),(3,10),(3,11),(4,7),(4,9),(4,11),(5,6),(5,9),(5,10),(6,13),(6,14),(7,13),(7,15),(8,14),(8,15),(9,13),(9,16),(10,14),(10,16),(11,15),(11,16),(12,6),(12,7),(12,8),(13,17),(14,17),(15,17),(16,17)],18)
 => ([(0,1),(0,2),(1,12),(2,3),(2,4),(2,5),(2,12),(3,8),(3,10),(3,11),(4,7),(4,9),(4,11),(5,6),(5,9),(5,10),(6,13),(6,14),(7,13),(7,15),(8,14),(8,15),(9,13),(9,16),(10,14),(10,16),(11,15),(11,16),(12,6),(12,7),(12,8),(13,17),(14,17),(15,17),(16,17)],18)
 => ([(0,1),(0,17),(1,16),(2,3),(2,4),(2,5),(2,6),(3,7),(3,8),(3,9),(4,9),(4,11),(4,12),(5,8),(5,10),(5,12),(6,7),(6,10),(6,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,17)],18)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ([(0,16),(1,5),(1,9),(1,10),(1,11),(2,5),(2,7),(2,8),(2,11),(3,5),(3,6),(3,8),(3,10),(4,5),(4,6),(4,7),(4,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,5),(1,9),(1,10),(2,6),(2,8),(3,6),(3,7),(4,1),(4,7),(4,8),(5,2),(5,3),(5,4),(6,12),(7,9),(7,12),(8,10),(8,12),(9,11),(10,11),(12,11)],13)
 => ([(0,5),(1,9),(1,10),(2,6),(2,8),(3,6),(3,7),(4,1),(4,7),(4,8),(5,2),(5,3),(5,4),(6,12),(7,9),(7,12),(8,10),(8,12),(9,11),(10,11),(12,11)],13)
 => ([(0,12),(1,3),(1,4),(1,10),(2,3),(2,4),(2,9),(3,8),(4,11),(5,6),(5,7),(5,8),(6,9),(6,12),(7,10),(7,12),(8,9),(8,10),(9,11),(10,11),(11,12)],13)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11)
 => ([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11)
 => ([(0,10),(1,2),(1,8),(2,9),(3,4),(3,5),(3,10),(4,7),(4,8),(5,6),(5,8),(6,9),(6,10),(7,9),(7,10),(8,9)],11)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,9),(1,8),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,9),(6,9),(7,9)],10)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1),(0,2),(1,11),(2,3),(2,4),(2,11),(3,8),(3,10),(4,5),(4,9),(4,10),(5,6),(5,7),(6,13),(7,13),(8,12),(9,7),(9,12),(10,6),(10,12),(11,8),(11,9),(12,13)],14)
 => ([(0,1),(0,2),(1,11),(2,3),(2,4),(2,11),(3,8),(3,10),(4,5),(4,9),(4,10),(5,6),(5,7),(6,13),(7,13),(8,12),(9,7),(9,12),(10,6),(10,12),(11,8),(11,9),(12,13)],14)
 => ([(0,1),(0,13),(1,12),(2,3),(2,4),(2,8),(3,5),(3,9),(4,5),(4,10),(5,11),(6,7),(6,8),(6,12),(7,9),(7,13),(8,9),(8,10),(9,11),(10,11),(10,12),(11,13),(12,13)],14)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => ([(0,8),(1,8),(1,10),(2,3),(2,4),(2,5),(3,6),(3,7),(4,7),(4,10),(5,6),(5,10),(6,9),(7,9),(8,9),(9,10)],11)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,9),(1,10),(2,8),(2,10),(3,7),(4,6),(5,1),(5,2),(5,6),(6,8),(6,9),(8,11),(9,11),(10,3),(10,11),(11,7)],12)
 => ([(0,4),(0,5),(1,9),(1,10),(2,8),(2,10),(3,7),(4,6),(5,1),(5,2),(5,6),(6,8),(6,9),(8,11),(9,11),(10,3),(10,11),(11,7)],12)
 => ([(0,3),(0,11),(1,2),(1,8),(2,9),(3,10),(4,7),(4,8),(4,10),(5,6),(5,8),(5,10),(6,9),(6,11),(7,9),(7,11),(8,9),(10,11)],12)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => 28 = 27 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ([(0,8),(1,5),(1,7),(2,4),(2,6),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,9),(7,9)],10)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16)
 => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16)
 => ([(0,6),(0,7),(0,15),(1,3),(1,4),(1,10),(2,3),(2,4),(2,9),(3,8),(4,12),(5,6),(5,7),(5,11),(6,13),(7,14),(8,9),(8,10),(8,11),(9,12),(9,13),(10,12),(10,14),(11,13),(11,14),(12,15),(13,15),(14,15)],16)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,3),(0,4),(1,6),(1,9),(2,6),(2,8),(3,7),(4,5),(4,7),(5,1),(5,2),(5,10),(6,11),(7,10),(8,11),(9,11),(10,8),(10,9)],12)
 => ([(0,3),(0,4),(1,6),(1,9),(2,6),(2,8),(3,7),(4,5),(4,7),(5,1),(5,2),(5,10),(6,11),(7,10),(8,11),(9,11),(10,8),(10,9)],12)
 => ([(0,1),(0,9),(1,8),(2,3),(2,4),(2,5),(3,6),(3,7),(4,7),(4,10),(5,6),(5,10),(6,11),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,9),(7,9),(8,9)],10)
 => ([(0,4),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,9),(7,9),(8,9)],10)
 => ([(0,1),(1,9),(2,3),(2,4),(2,5),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,9),(7,9),(8,9)],10)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,16),(7,16),(8,1),(8,17),(8,18),(9,14),(9,17),(10,15),(10,17),(11,14),(11,18),(12,15),(12,18),(13,14),(13,15),(14,19),(15,19),(17,6),(17,19),(18,7),(18,19),(19,16)],20)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,16),(7,16),(8,1),(8,17),(8,18),(9,14),(9,17),(10,15),(10,17),(11,14),(11,18),(12,15),(12,18),(13,14),(13,15),(14,19),(15,19),(17,6),(17,19),(18,7),(18,19),(19,16)],20)
 => ([(0,2),(0,3),(0,19),(1,2),(1,3),(1,18),(2,17),(3,16),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,10),(5,11),(6,12),(6,13),(7,14),(7,15),(8,13),(8,15),(8,16),(9,12),(9,14),(9,16),(10,12),(10,14),(10,17),(11,13),(11,15),(11,17),(12,18),(13,18),(14,19),(15,19),(16,18),(16,19),(17,18),(17,19)],20)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12)
 => ([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12)
 => ([(0,1),(0,9),(1,8),(2,3),(2,4),(2,5),(3,6),(3,7),(4,7),(4,10),(5,6),(5,10),(6,11),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,7),(5,7),(6,7)],8)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(2,8),(2,9),(3,9),(3,11),(3,12),(4,8),(4,10),(4,12),(5,7),(5,10),(5,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,1),(16,17),(17,6)],18)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(2,8),(2,9),(3,9),(3,11),(3,12),(4,8),(4,10),(4,12),(5,7),(5,10),(5,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,1),(16,17),(17,6)],18)
 => ([(0,1),(0,17),(1,16),(2,3),(2,4),(2,5),(2,6),(3,7),(3,8),(3,9),(4,9),(4,11),(4,12),(5,8),(5,10),(5,12),(6,7),(6,10),(6,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,17)],18)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,2),(0,3),(0,4),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,1),(6,9),(7,9),(8,9),(9,5)],10)
 => ([(0,2),(0,3),(0,4),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,1),(6,9),(7,9),(8,9),(9,5)],10)
 => ([(0,1),(1,9),(2,3),(2,4),(2,5),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,9),(7,9),(8,9)],10)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ([(0,16),(1,5),(1,9),(1,10),(1,11),(2,5),(2,7),(2,8),(2,11),(3,5),(3,6),(3,8),(3,10),(4,5),(4,6),(4,7),(4,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,10),(2,7),(2,8),(3,9),(3,12),(4,9),(4,11),(5,2),(5,11),(5,12),(7,14),(8,14),(9,1),(9,13),(10,6),(11,7),(11,13),(12,8),(12,13),(13,10),(13,14),(14,6)],15)
 => ([(0,3),(0,4),(0,5),(1,10),(2,7),(2,8),(3,9),(3,12),(4,9),(4,11),(5,2),(5,11),(5,12),(7,14),(8,14),(9,1),(9,13),(10,6),(11,7),(11,13),(12,8),(12,13),(13,10),(13,14),(14,6)],15)
 => ([(0,8),(0,13),(1,8),(1,12),(2,4),(2,5),(2,11),(3,6),(3,7),(3,11),(4,10),(4,12),(5,9),(5,12),(6,9),(6,13),(7,10),(7,13),(8,14),(9,11),(9,14),(10,11),(10,14),(12,14),(13,14)],15)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13)
 => ([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13)
 => ([(0,8),(0,9),(1,9),(1,11),(2,8),(2,10),(3,5),(3,6),(3,7),(4,5),(4,6),(4,12),(5,10),(6,11),(7,10),(7,11),(8,12),(9,12),(10,12),(11,12)],13)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(3,10),(4,6),(4,10),(5,6),(5,7),(6,11),(7,11),(8,9),(10,2),(10,11),(11,1),(11,8)],12)
 => ([(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(3,10),(4,6),(4,10),(5,6),(5,7),(6,11),(7,11),(8,9),(10,2),(10,11),(11,1),(11,8)],12)
 => ([(0,9),(0,10),(1,2),(1,9),(2,11),(3,4),(3,5),(3,6),(4,7),(4,8),(5,8),(5,11),(6,7),(6,11),(7,10),(8,10),(9,11),(10,11)],12)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11)
 => ([(0,2),(0,10),(1,2),(1,10),(3,4),(3,5),(3,6),(4,8),(4,9),(5,7),(5,9),(6,7),(6,8),(7,10),(8,10),(9,10)],11)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => 28 = 27 + 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ([(0,8),(1,8),(1,10),(2,3),(2,4),(2,5),(3,6),(3,7),(4,7),(4,10),(5,6),(5,10),(6,9),(7,9),(8,9),(9,10)],11)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,1),(12,13),(13,8)],14)
 => ([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,1),(12,13),(13,8)],14)
 => ([(0,1),(0,12),(1,13),(2,5),(2,6),(2,13),(3,5),(3,6),(3,11),(4,7),(4,8),(4,11),(5,10),(6,9),(7,9),(7,12),(8,10),(8,12),(9,11),(9,13),(10,11),(10,13),(12,13)],14)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(2,10),(3,6),(3,8),(4,6),(4,7),(5,2),(5,7),(5,8),(6,11),(7,9),(7,11),(8,10),(8,11),(9,12),(10,12),(11,12),(12,1)],13)
 => ([(0,3),(0,4),(0,5),(2,9),(2,10),(3,6),(3,8),(4,6),(4,7),(5,2),(5,7),(5,8),(6,11),(7,9),(7,11),(8,10),(8,11),(9,12),(10,12),(11,12),(12,1)],13)
 => ([(0,12),(1,3),(1,4),(1,10),(2,3),(2,4),(2,9),(3,8),(4,11),(5,6),(5,7),(5,8),(6,9),(6,12),(7,10),(7,12),(8,9),(8,10),(9,11),(10,11),(11,12)],13)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,8),(1,10),(2,7),(2,9),(3,11),(3,12),(4,2),(4,11),(4,13),(5,1),(5,12),(5,13),(6,17),(7,15),(8,16),(9,6),(9,15),(10,6),(10,16),(11,7),(11,14),(12,8),(12,14),(13,9),(13,10),(13,14),(14,15),(14,16),(15,17),(16,17)],18)
 => ([(0,3),(0,4),(0,5),(1,8),(1,10),(2,7),(2,9),(3,11),(3,12),(4,2),(4,11),(4,13),(5,1),(5,12),(5,13),(6,17),(7,15),(8,16),(9,6),(9,15),(10,6),(10,16),(11,7),(11,14),(12,8),(12,14),(13,9),(13,10),(13,14),(14,15),(14,16),(15,17),(16,17)],18)
 => ([(0,7),(0,10),(0,11),(1,4),(1,8),(1,9),(2,6),(2,9),(2,11),(3,5),(3,8),(3,10),(4,12),(4,13),(5,12),(5,14),(6,13),(6,15),(7,14),(7,15),(8,12),(8,17),(9,13),(9,17),(10,14),(10,17),(11,15),(11,17),(12,16),(13,16),(14,16),(15,16),(16,17)],18)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,8),(2,10),(3,9),(3,11),(4,9),(4,12),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,15),(10,6),(10,13),(11,8),(11,15),(12,1),(12,10),(12,15),(13,14),(15,7),(15,13)],16)
 => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,8),(2,10),(3,9),(3,11),(4,9),(4,12),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,15),(10,6),(10,13),(11,8),(11,15),(12,1),(12,10),(12,15),(13,14),(15,7),(15,13)],16)
 => ([(0,3),(0,5),(0,14),(1,2),(1,4),(1,14),(2,6),(2,15),(3,7),(3,15),(4,6),(4,10),(5,7),(5,11),(6,12),(7,13),(8,9),(8,12),(8,13),(9,10),(9,11),(10,12),(10,14),(11,13),(11,14),(12,15),(13,15),(14,15)],16)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11)
 => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11)
 => ([(0,1),(0,9),(1,8),(2,5),(2,9),(3,5),(3,6),(4,6),(4,7),(5,10),(6,10),(7,8),(7,10),(8,9),(9,10)],11)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(1,8),(2,6),(2,7),(3,10),(3,11),(4,9),(4,11),(5,9),(5,10),(6,12),(7,12),(8,12),(9,13),(10,13),(11,1),(11,2),(11,13),(13,7),(13,8)],14)
 => ([(0,3),(0,4),(0,5),(1,6),(1,8),(2,6),(2,7),(3,10),(3,11),(4,9),(4,11),(5,9),(5,10),(6,12),(7,12),(8,12),(9,13),(10,13),(11,1),(11,2),(11,13),(13,7),(13,8)],14)
 => ([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,8),(2,9),(3,10),(3,11),(4,9),(4,13),(5,8),(5,13),(6,11),(6,13),(7,10),(7,13),(8,12),(9,12),(10,12),(11,12),(12,13)],14)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(0,1),(0,2),(1,8),(2,8),(3,4),(3,6),(4,7),(5,6),(5,8),(6,7),(7,8)],9)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(0,3),(0,9),(1,2),(1,6),(2,8),(3,5),(4,5),(4,7),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,2),(0,3),(1,11),(2,1),(2,12),(3,4),(3,5),(3,12),(4,8),(4,10),(5,8),(5,9),(6,14),(7,14),(8,13),(9,6),(9,13),(10,7),(10,13),(11,6),(11,7),(12,9),(12,10),(12,11),(13,14)],15)
 => ([(0,2),(0,3),(1,11),(2,1),(2,12),(3,4),(3,5),(3,12),(4,8),(4,10),(5,8),(5,9),(6,14),(7,14),(8,13),(9,6),(9,13),(10,7),(10,13),(11,6),(11,7),(12,9),(12,10),(12,11),(13,14)],15)
 => ([(0,8),(0,13),(1,8),(1,12),(2,4),(2,5),(2,11),(3,6),(3,7),(3,11),(4,10),(4,12),(5,9),(5,12),(6,9),(6,13),(7,10),(7,13),(8,14),(9,11),(9,14),(10,11),(10,14),(12,14),(13,14)],15)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1),(0,2),(1,11),(2,4),(2,5),(2,11),(3,6),(3,7),(4,8),(4,10),(5,8),(5,9),(6,13),(7,13),(8,12),(9,6),(9,12),(10,7),(10,12),(11,3),(11,9),(11,10),(12,13)],14)
 => ([(0,1),(0,2),(1,11),(2,4),(2,5),(2,11),(3,6),(3,7),(4,8),(4,10),(5,8),(5,9),(6,13),(7,13),(8,12),(9,6),(9,12),(10,7),(10,12),(11,3),(11,9),(11,10),(12,13)],14)
 => ([(0,1),(0,12),(1,13),(2,5),(2,6),(2,13),(3,5),(3,6),(3,11),(4,7),(4,8),(4,11),(5,10),(6,9),(7,9),(7,12),(8,10),(8,12),(9,11),(9,13),(10,11),(10,13),(12,13)],14)
 => ? ∊ {33,33,33,34,34,34,39,39,40,40,41,41,45,46,46,46,46,46,47,47,48,53,53,53,53,54,54,56,56,60,60,60,60,61,63,63,67,67,70,70,75,75,77,77,78,84,84,90,93,98,98,108,108,108,126,126,162,243} + 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => 28 = 27 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 22 = 21 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => 28 = 27 + 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 29 = 28 + 1
Description
The number of convex subsets of vertices in a graph. A set of vertices $U$ is convex, if for any two vertices $u, v\in U$, all vertices on any shortest path connecting $u$ and $v$ are also in $U$.