Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001754
Mapping
St001754: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([(0,1)],2)
 => 2
([(0,2),(2,1)],3)
 => 5
([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,3),(2,1),(3,2)],4)
 => 14
([(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)
 => 5
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 13
([(0,4),(2,3),(3,1),(4,2)],5)
 => 42
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 13
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => 3
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => 3
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => 8
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 17
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 48
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 8
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 42
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => 3
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 42
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => 8
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 7
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 10
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 132
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => 17
Description
The number of tolerances of a finite lattice. Let $L$ be a lattice. A tolerance $\tau$ is a reflexive and symmetric relation on $L$ which is compatible with meet and join. Equivalently, a tolerance of $L$ is the image of a congruence by a surjective lattice homomorphism onto $L$. The number of tolerances of a chain of $n$ elements is the Catalan number $\frac{1}{n+1}\binom{2n}{n}$, see [2].
Matching statistic: St000741
Mapping
Mp00197: Lattices —lattice of congruences⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000741: Graphs ⟶ ℤResult quality: 21% ●values known / values provided: 28%●distinct values known / distinct values provided: 21%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(2,1)],3)
 => ([(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)
 => ? = 5 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(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)
 => ? ∊ {4,14} - 1
([(0,3),(2,1),(3,2)],4)
 => ([(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)
 => ? ∊ {4,14} - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(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)
 => ? ∊ {5,13,13,42} - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(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)
 => ? ∊ {5,13,13,42} - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(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)
 => ? ∊ {5,13,13,42} - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(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)
 => ? ∊ {5,13,13,42} - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(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)
 => ? ∊ {7,8,8,8,10,17,17,42,42,48,132} - 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(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)
 => ? ∊ {7,8,8,8,10,17,17,42,42,48,132} - 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(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)
 => ? ∊ {7,8,8,8,10,17,17,42,42,48,132} - 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(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)
 => ? ∊ {7,8,8,8,10,17,17,42,42,48,132} - 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(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)
 => ? ∊ {7,8,8,8,10,17,17,42,42,48,132} - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(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)
 => ? ∊ {7,8,8,8,10,17,17,42,42,48,132} - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(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)
 => ? ∊ {7,8,8,8,10,17,17,42,42,48,132} - 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(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)
 => ? ∊ {7,8,8,8,10,17,17,42,42,48,132} - 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(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)
 => ? ∊ {7,8,8,8,10,17,17,42,42,48,132} - 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,29),(16,30),(17,26),(17,30),(18,27),(18,30),(19,28),(19,30),(20,26),(20,29),(21,27),(21,29),(22,28),(22,29),(23,26),(23,28),(24,27),(24,28),(25,26),(25,27),(26,31),(27,31),(28,31),(29,31),(30,31)],32)
 => ([(0,27),(0,28),(0,29),(0,30),(0,31),(1,6),(1,13),(1,14),(1,15),(1,16),(2,6),(2,10),(2,11),(2,12),(2,16),(3,6),(3,8),(3,9),(3,12),(3,15),(4,6),(4,7),(4,9),(4,11),(4,14),(5,6),(5,7),(5,8),(5,10),(5,13),(7,17),(7,20),(7,23),(8,17),(8,18),(8,21),(9,17),(9,19),(9,22),(10,18),(10,20),(10,24),(11,19),(11,20),(11,25),(12,18),(12,19),(12,26),(13,21),(13,23),(13,24),(14,22),(14,23),(14,25),(15,21),(15,22),(15,26),(16,24),(16,25),(16,26),(17,30),(17,31),(18,27),(18,31),(19,28),(19,31),(20,29),(20,31),(21,27),(21,30),(22,28),(22,30),(23,29),(23,30),(24,27),(24,29),(25,28),(25,29),(26,27),(26,28)],32)
 => ? ∊ {7,8,8,8,10,17,17,42,42,48,132} - 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(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)
 => ? ∊ {7,8,8,8,10,17,17,42,42,48,132} - 1
Description
The Colin de Verdière graph invariant.