Your data matches 7 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000860
Mapping
St000860: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => 2 = 1 + 1
['A',2]
 => 1 = 0 + 1
['B',2]
 => 2 = 1 + 1
['G',2]
 => 2 = 1 + 1
['A',3]
 => 1 = 0 + 1
['B',3]
 => 2 = 1 + 1
['C',3]
 => 2 = 1 + 1
['A',4]
 => 1 = 0 + 1
['B',4]
 => 2 = 1 + 1
['C',4]
 => 2 = 1 + 1
['D',4]
 => 2 = 1 + 1
['A',5]
 => 1 = 0 + 1
Description
The size of the center of the Weyl group of a finite Cartan type.
Matching statistic: St001939
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00313: Integer partitions —Glaisher-Franklin inverse⟶ Integer partitions
St001939: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => [1]
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [1,1,1]
 => 0
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [3,1]
 => 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [5,1]
 => 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [3,1,1,1]
 => 0
['B',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => [5,3,1]
 => [5,3,1]
 => 1
['C',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => [5,3,1]
 => [5,3,1]
 => 1
['A',4]
 => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10)
 => [4,3,2,1]
 => [3,1,1,1,1,1,1,1]
 => 0
['B',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => [7,5,3,1]
 => [7,5,3,1]
 => 1
['C',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => [7,5,3,1]
 => [7,5,3,1]
 => 1
['D',4]
 => ([(0,10),(1,9),(2,8),(3,8),(3,9),(3,10),(5,11),(6,11),(7,11),(8,5),(8,6),(9,5),(9,7),(10,6),(10,7),(11,4)],12)
 => [5,3,3,1]
 => [6,5,1]
 => 1
['A',5]
 => ([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15)
 => [5,4,3,2,1]
 => [5,3,1,1,1,1,1,1,1]
 => 0
Description
The number of parts that are equal to their multiplicity in the integer partition.
Matching statistic: St001940
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00313: Integer partitions —Glaisher-Franklin inverse⟶ Integer partitions
St001940: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => [1]
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [1,1,1]
 => 0
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [3,1]
 => 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [5,1]
 => 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [3,1,1,1]
 => 0
['B',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => [5,3,1]
 => [5,3,1]
 => 1
['C',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => [5,3,1]
 => [5,3,1]
 => 1
['A',4]
 => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10)
 => [4,3,2,1]
 => [3,1,1,1,1,1,1,1]
 => 0
['B',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => [7,5,3,1]
 => [7,5,3,1]
 => 1
['C',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => [7,5,3,1]
 => [7,5,3,1]
 => 1
['D',4]
 => ([(0,10),(1,9),(2,8),(3,8),(3,9),(3,10),(5,11),(6,11),(7,11),(8,5),(8,6),(9,5),(9,7),(10,6),(10,7),(11,4)],12)
 => [5,3,3,1]
 => [6,5,1]
 => 1
['A',5]
 => ([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15)
 => [5,4,3,2,1]
 => [5,3,1,1,1,1,1,1,1]
 => 0
Description
The number of distinct parts that are equal to their multiplicity in the integer partition.
Matching statistic: St001568
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
St001568: Integer partitions ⟶ ℤResult quality: 58% ●values known / values provided: 58%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => [1]
 => ? = 1 + 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => 1 = 0 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => [2,1,1]
 => 2 = 1 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(4,5)],6)
 => [2,1,1,1,1]
 => 2 = 1 + 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => 1 = 0 + 1
['B',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => ([(2,7),(3,5),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9)
 => [7,1,1]
 => 2 = 1 + 1
['C',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => ([(2,7),(3,5),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9)
 => [7,1,1]
 => 2 = 1 + 1
['A',4]
 => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10)
 => ([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => [9,1]
 => 1 = 0 + 1
['B',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => ([(2,10),(3,6),(3,10),(3,13),(4,9),(4,11),(4,14),(4,15),(5,12),(5,13),(5,14),(5,15),(6,12),(6,14),(6,15),(7,8),(7,9),(7,12),(7,14),(7,15),(8,11),(8,13),(8,14),(8,15),(9,11),(9,13),(9,15),(10,12),(10,14),(10,15),(11,12),(11,14),(11,15),(12,13),(13,14),(13,15)],16)
 => [14,1,1]
 => ? = 1 + 1
['C',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => ([(2,10),(3,6),(3,10),(3,13),(4,9),(4,11),(4,14),(4,15),(5,12),(5,13),(5,14),(5,15),(6,12),(6,14),(6,15),(7,8),(7,9),(7,12),(7,14),(7,15),(8,11),(8,13),(8,14),(8,15),(9,11),(9,13),(9,15),(10,12),(10,14),(10,15),(11,12),(11,14),(11,15),(12,13),(13,14),(13,15)],16)
 => [14,1,1]
 => ? = 1 + 1
['D',4]
 => ([(0,10),(1,9),(2,8),(3,8),(3,9),(3,10),(5,11),(6,11),(7,11),(8,5),(8,6),(9,5),(9,7),(10,6),(10,7),(11,4)],12)
 => ([(2,9),(2,10),(2,11),(3,4),(3,5),(3,8),(3,11),(4,5),(4,7),(4,10),(5,6),(5,9),(6,7),(6,8),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
 => [10,1,1]
 => ? = 1 + 1
['A',5]
 => ([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15)
 => ([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => [14,1]
 => ? = 0 + 1
Description
The smallest positive integer that does not appear twice in the partition.
Matching statistic: St001057
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
St001057: Graphs ⟶ ℤResult quality: 42% ●values known / values provided: 42%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 0
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(4,5)],6)
 => ([(4,5)],6)
 => 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
['B',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => ([(2,7),(3,5),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,6),(3,7),(3,8),(4,5),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 1
['C',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => ([(2,7),(3,5),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(2,6),(3,7),(3,8),(4,5),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 1
['A',4]
 => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10)
 => ([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 0
['B',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => ([(2,10),(3,6),(3,10),(3,13),(4,9),(4,11),(4,14),(4,15),(5,12),(5,13),(5,14),(5,15),(6,12),(6,14),(6,15),(7,8),(7,9),(7,12),(7,14),(7,15),(8,11),(8,13),(8,14),(8,15),(9,11),(9,13),(9,15),(10,12),(10,14),(10,15),(11,12),(11,14),(11,15),(12,13),(13,14),(13,15)],16)
 => ([(2,7),(3,12),(3,13),(3,14),(3,15),(4,10),(4,13),(4,14),(4,15),(5,8),(5,11),(5,13),(5,14),(5,15),(6,9),(6,11),(6,13),(6,14),(6,15),(7,10),(7,13),(7,14),(7,15),(8,9),(8,12),(8,13),(8,14),(8,15),(9,11),(9,13),(9,14),(9,15),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,14),(11,15),(12,13),(12,14),(12,15),(13,14),(13,15),(14,15)],16)
 => ? = 1
['C',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => ([(2,10),(3,6),(3,10),(3,13),(4,9),(4,11),(4,14),(4,15),(5,12),(5,13),(5,14),(5,15),(6,12),(6,14),(6,15),(7,8),(7,9),(7,12),(7,14),(7,15),(8,11),(8,13),(8,14),(8,15),(9,11),(9,13),(9,15),(10,12),(10,14),(10,15),(11,12),(11,14),(11,15),(12,13),(13,14),(13,15)],16)
 => ([(2,7),(3,12),(3,13),(3,14),(3,15),(4,10),(4,13),(4,14),(4,15),(5,8),(5,11),(5,13),(5,14),(5,15),(6,9),(6,11),(6,13),(6,14),(6,15),(7,10),(7,13),(7,14),(7,15),(8,9),(8,12),(8,13),(8,14),(8,15),(9,11),(9,13),(9,14),(9,15),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,14),(11,15),(12,13),(12,14),(12,15),(13,14),(13,15),(14,15)],16)
 => ? = 1
['D',4]
 => ([(0,10),(1,9),(2,8),(3,8),(3,9),(3,10),(5,11),(6,11),(7,11),(8,5),(8,6),(9,5),(9,7),(10,6),(10,7),(11,4)],12)
 => ([(2,9),(2,10),(2,11),(3,4),(3,5),(3,8),(3,11),(4,5),(4,7),(4,10),(5,6),(5,9),(6,7),(6,8),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
 => ([(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
 => ? = 1
['A',5]
 => ([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15)
 => ([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(1,12),(1,13),(1,14),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(2,12),(2,13),(2,14),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(3,12),(3,13),(3,14),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(5,12),(5,13),(5,14),(6,7),(6,8),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(7,14),(8,9),(8,10),(8,11),(8,12),(8,13),(8,14),(9,10),(9,11),(9,12),(9,13),(9,14),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14),(12,13),(12,14),(13,14)],15)
 => ? = 0
Description
The Grundy value of the game of creating an independent set in a graph. Two players alternately add a vertex to an initially empty set, which is not adjacent to any of the vertices it already contains. Alternatively, the game can be described as starting with a graph, the players remove vertices together with their neighbors, until the graph is empty.
Matching statistic: St000667
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000667: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 33%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [2]
 => 2 = 1 + 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [3,2]
 => 1 = 0 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 2 = 1 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => 2 = 1 + 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [8,4,2]
 => ? = 0 + 1
['B',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => [6,6,6,2]
 => ? = 1 + 1
['C',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => [6,6,6,2]
 => ? = 1 + 1
['A',4]
 => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10)
 => [10,10,10,5,5,2]
 => ? = 0 + 1
['B',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => [8,8,8,8,8,8,8,8,4,2]
 => ? = 1 + 1
['C',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => [8,8,8,8,8,8,8,8,4,2]
 => ? = 1 + 1
['D',4]
 => ([(0,10),(1,9),(2,8),(3,8),(3,9),(3,10),(5,11),(6,11),(7,11),(8,5),(8,6),(9,5),(9,7),(10,6),(10,7),(11,4)],12)
 => [6,6,6,6,6,6,6,3,3,2]
 => ? = 1 + 1
['A',5]
 => ([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15)
 => [12,12,12,12,12,12,12,12,12,6,6,6,4,2]
 => ? = 0 + 1
Description
The greatest common divisor of the parts of the partition.
Matching statistic: St000755
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000755: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 33%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [2]
 => 2 = 1 + 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [3,2]
 => 1 = 0 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 2 = 1 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => 2 = 1 + 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [8,4,2]
 => ? = 0 + 1
['B',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => [6,6,6,2]
 => ? = 1 + 1
['C',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => [6,6,6,2]
 => ? = 1 + 1
['A',4]
 => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10)
 => [10,10,10,5,5,2]
 => ? = 0 + 1
['B',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => [8,8,8,8,8,8,8,8,4,2]
 => ? = 1 + 1
['C',4]
 => ([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => [8,8,8,8,8,8,8,8,4,2]
 => ? = 1 + 1
['D',4]
 => ([(0,10),(1,9),(2,8),(3,8),(3,9),(3,10),(5,11),(6,11),(7,11),(8,5),(8,6),(9,5),(9,7),(10,6),(10,7),(11,4)],12)
 => [6,6,6,6,6,6,6,3,3,2]
 => ? = 1 + 1
['A',5]
 => ([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15)
 => [12,12,12,12,12,12,12,12,12,6,6,6,4,2]
 => ? = 0 + 1
Description
The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. Consider the recurrence $$f(n)=\sum_{p\in\lambda} f(n-p).$$ This statistic returns the number of distinct real roots of the associated characteristic polynomial. For example, the partition $(2,1)$ corresponds to the recurrence $f(n)=f(n-1)+f(n-2)$ with associated characteristic polynomial $x^2-x-1$, which has two real roots.