Your data matches 46 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001878
Mapping
Mp00243: Graphs ā€”weak duplicate orderāŸ¶ Posets
Mp00125: Posets ā€”dual posetāŸ¶ Posets
Mp00205: Posets ā€”maximal antichainsāŸ¶ Lattices
St001878: Lattices āŸ¶ ā„¤Result quality: 100% ā—values known / values provided: 100%ā—distinct values known / distinct values provided: 100%
Values
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3)],5)
 => ([(0,4),(1,2),(1,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4)],6)
 => ([(0,5),(1,5),(2,3),(2,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(0,2),(2,1)],3)
 => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4)],6)
 => ([(0,5),(1,2),(1,3),(1,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(4,5)],6)
 => ([(0,4),(1,3),(1,5),(5,2)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => ([(0,3),(0,5),(1,4),(1,5),(4,2)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(4,3),(5,2)],6)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,5)],6)
 => ([(2,5),(3,4),(3,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,3)],5)
 => ([(0,4),(1,2),(1,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => ([(0,2),(2,1)],3)
 => 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,3)],5)
 => ([(0,4),(1,2),(1,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(4,5)],6)
 => ([(0,4),(1,3),(1,5),(5,2)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,3),(5,4)],6)
 => ([(0,4),(1,5),(5,2),(5,3)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([(0,2),(2,1)],3)
 => 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(4,5)],6)
 => ([(1,4),(1,5),(5,2),(5,3)],6)
 => ([(0,2),(2,1)],3)
 => 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
Matching statistic: St001217
(load all 8 compositions to match this statistic)
Mapping
Mp00247: Graphs ā€”de-duplicateāŸ¶ Graphs
Mp00037: Graphs ā€”to partition of connected componentsāŸ¶ Integer partitions
Mp00043: Integer partitions ā€”to Dyck pathāŸ¶ Dyck paths
St001217: Dyck paths āŸ¶ ā„¤Result quality: 25% ā—values known / values provided: 25%ā—distinct values known / distinct values provided: 100%
Values
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(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)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => 0 = 1 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => 0 = 1 - 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 2 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 2 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 1 - 1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 1 - 1
Description
The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1.
Matching statistic: St000260
(load all 6 compositions to match this statistic)
Mapping
Mp00147: Graphs ā€”squareāŸ¶ Graphs
Mp00111: Graphs ā€”complementāŸ¶ Graphs
St000260: Graphs āŸ¶ ā„¤Result quality: 22% ā—values known / values provided: 22%ā—distinct values known / distinct values provided: 100%
Values
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3),(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)
 => ? = 2
([(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),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ? = 2
([(0,4),(1,3),(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)
 => ([(3,4)],5)
 => ? = 2
([(0,1),(0,4),(1,3),(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)
 => ? = 2
([(0,3),(0,4),(1,2),(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)
 => ? = 2
([(0,4),(1,2),(1,3),(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)
 => ([(3,4)],5)
 => ? = 2
([(2,5),(3,4),(4,5)],6)
 => ([(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)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(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)
 => ([(2,5),(3,5),(4,5)],6)
 => ? = 2
([(1,5),(2,5),(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)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,5),(2,4),(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)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(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)
 => ([(3,5),(4,5)],6)
 => ? = 2
([(1,5),(2,4),(2,5),(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)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ([(3,5),(4,5)],6)
 => ? = 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],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)
 => ([(4,5)],6)
 => ? = 2
([(0,5),(1,4),(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)
 => ([(4,5)],6)
 => ? = 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(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)],6)
 => 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ? = 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(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)
 => ([(2,5),(3,5),(4,5)],6)
 => ? = 2
([(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)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1
([(1,5),(2,3),(2,4),(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)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ? = 2
([(0,5),(1,2),(1,5),(2,4),(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)
 => ([(4,5)],6)
 => ? = 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ([(3,5),(4,5)],6)
 => ? = 2
([(1,4),(1,5),(2,3),(2,5),(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)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ([(3,5),(4,5)],6)
 => ? = 2
([(1,5),(2,3),(2,4),(2,5),(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)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ([(3,5),(4,5)],6)
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(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)
 => ([(4,5)],6)
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],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)
 => ([(4,5)],6)
 => ? = 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(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)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1
([(0,5),(1,4),(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)
 => ([(4,5)],6)
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(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)
 => ([(3,5),(4,5)],6)
 => ? = 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(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)
 => ([(4,5)],6)
 => ? = 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ([(3,5),(4,5)],6)
 => ? = 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(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)
 => ([(3,5),(4,5)],6)
 => ? = 1
([(0,1),(0,5),(1,3),(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)
 => ([(4,5)],6)
 => ? = 2
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(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)
 => ([(3,5),(4,5)],6)
 => ? = 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],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)
 => ([(4,5)],6)
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(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)
 => ([(4,5)],6)
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 2
([(0,5),(1,2),(1,3),(1,4),(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)
 => ([(4,5)],6)
 => ? = 2
([(0,5),(1,3),(1,4),(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)
 => ([(4,5)],6)
 => ? = 2
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 2
([(0,3),(0,5),(1,2),(1,4),(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)
 => ([(4,5)],6)
 => ? = 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 2
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 2
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 2
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(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)
 => ([],6)
 => ? = 2
([(3,6),(4,5),(5,6)],7)
 => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => 2
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000755
Mapping
Mp00037: Graphs ā€”to partition of connected componentsāŸ¶ Integer partitions
Mp00202: Integer partitions ā€”first row removalāŸ¶ Integer partitions
Mp00321: Integer partitions ā€”2-conjugateāŸ¶ Integer partitions
St000755: Integer partitions āŸ¶ ā„¤Result quality: 21% ā—values known / values provided: 21%ā—distinct values known / distinct values provided: 100%
Values
([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ?
 => ? = 2
([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [1,1]
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [1,1]
 => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => [2]
 => 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2
([(3,6),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [1,1,1]
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [1,1,1]
 => 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [3]
 => 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [5,2]
 => [2]
 => [2]
 => 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [3]
 => 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 1
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 1
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 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.
Matching statistic: St001914
Mapping
Mp00247: Graphs ā€”de-duplicateāŸ¶ Graphs
Mp00037: Graphs ā€”to partition of connected componentsāŸ¶ Integer partitions
Mp00202: Integer partitions ā€”first row removalāŸ¶ Integer partitions
St001914: Integer partitions āŸ¶ ā„¤Result quality: 21% ā—values known / values provided: 21%ā—distinct values known / distinct values provided: 100%
Values
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(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)
 => [5]
 => []
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(1,2),(3,6),(4,5),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1
Description
The size of the orbit of an integer partition in Bulgarian solitaire. Bulgarian solitaire is the dynamical system where a move consists of removing the first column of the Ferrers diagram and inserting it as a row. This statistic returns the number of partitions that can be obtained from the given partition.
Matching statistic: St000142
Mapping
Mp00037: Graphs ā€”to partition of connected componentsāŸ¶ Integer partitions
Mp00202: Integer partitions ā€”first row removalāŸ¶ Integer partitions
Mp00321: Integer partitions ā€”2-conjugateāŸ¶ Integer partitions
St000142: Integer partitions āŸ¶ ā„¤Result quality: 21% ā—values known / values provided: 21%ā—distinct values known / distinct values provided: 100%
Values
([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => [2]
 => 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(3,6),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [3]
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [5,2]
 => [2]
 => [2]
 => 1 = 2 - 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [3]
 => 0 = 1 - 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
Description
The number of even parts of a partition.
Matching statistic: St001092
Mapping
Mp00037: Graphs ā€”to partition of connected componentsāŸ¶ Integer partitions
Mp00202: Integer partitions ā€”first row removalāŸ¶ Integer partitions
Mp00321: Integer partitions ā€”2-conjugateāŸ¶ Integer partitions
St001092: Integer partitions āŸ¶ ā„¤Result quality: 21% ā—values known / values provided: 21%ā—distinct values known / distinct values provided: 100%
Values
([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => [2]
 => 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(3,6),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [3]
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [5,2]
 => [2]
 => [2]
 => 1 = 2 - 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [3]
 => 0 = 1 - 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
Description
The number of distinct even parts of a partition. See Section 3.3.1 of [1].
Matching statistic: St001252
Mapping
Mp00037: Graphs ā€”to partition of connected componentsāŸ¶ Integer partitions
Mp00202: Integer partitions ā€”first row removalāŸ¶ Integer partitions
Mp00321: Integer partitions ā€”2-conjugateāŸ¶ Integer partitions
St001252: Integer partitions āŸ¶ ā„¤Result quality: 21% ā—values known / values provided: 21%ā—distinct values known / distinct values provided: 100%
Values
([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => [2]
 => 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(3,6),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [3]
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [5,2]
 => [2]
 => [2]
 => 1 = 2 - 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [3]
 => 0 = 1 - 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
Description
Half the sum of the even parts of a partition.
Matching statistic: St001587
Mapping
Mp00037: Graphs ā€”to partition of connected componentsāŸ¶ Integer partitions
Mp00202: Integer partitions ā€”first row removalāŸ¶ Integer partitions
Mp00321: Integer partitions ā€”2-conjugateāŸ¶ Integer partitions
St001587: Integer partitions āŸ¶ ā„¤Result quality: 21% ā—values known / values provided: 21%ā—distinct values known / distinct values provided: 100%
Values
([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => [2]
 => 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(3,6),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [3]
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [5,2]
 => [2]
 => [2]
 => 1 = 2 - 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [3]
 => 0 = 1 - 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
Description
Half of the largest even part of an integer partition. The largest even part is recorded by [[St000995]].
Matching statistic: St001657
Mapping
Mp00037: Graphs ā€”to partition of connected componentsāŸ¶ Integer partitions
Mp00202: Integer partitions ā€”first row removalāŸ¶ Integer partitions
Mp00321: Integer partitions ā€”2-conjugateāŸ¶ Integer partitions
St001657: Integer partitions āŸ¶ ā„¤Result quality: 21% ā—values known / values provided: 21%ā—distinct values known / distinct values provided: 100%
Values
([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ?
 => ? = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => [2]
 => 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ?
 => ? = 2 - 1
([(3,6),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [1,1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [3]
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [5,2]
 => [2]
 => [2]
 => 1 = 2 - 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [3]
 => 0 = 1 - 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => [1]
 => 0 = 1 - 1
Description
The number of twos in an integer partition. The total number of twos in all partitions of $n$ is equal to the total number of singletons [[St001484]] in all partitions of $n-1$, see [1].
The following 36 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001730The number of times the path corresponding to a binary word crosses the base line. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001330The hat guessing number of a graph. St001060The distinguishing index of a graph. St000990The first ascent of a permutation. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001204Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{nāˆ’1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001188The number of simple modules $S$ with grade $\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra $A$ corresponding to the Dyck path. St001191Number of simple modules $S$ with $Ext_A^i(S,A)=0$ for all $i=0,1,...,g-1$ in the corresponding Nakayama algebra $A$ with global dimension $g$. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001256Number of simple reflexive modules that are 2-stable reflexive. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001193The dimension of $Ext_A^1(A/AeA,A)$ in the corresponding Nakayama algebra $A$ such that $eA$ is a minimal faithful projective-injective module. St001219Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive. St001651The Frankl number of a lattice. St000068The number of minimal elements in a poset. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St000934The 2-degree of an integer partition. St001568The smallest positive integer that does not appear twice in the partition. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000929The constant term of the character polynomial of an integer partition. St000264The girth of a graph, which is not a tree.