Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001876
Mapping
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001876: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,3,5],[2,4]]
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,2,4],[3,5]]
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,5],[2],[4]]
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,2,4],[3],[5]]
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3],[2,5],[4]]
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,2],[3,4],[5]]
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,2,3,5,6],[4]]
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,5,6],[2,4]]
 => [1,2,3] => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,4,6],[2,5]]
 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4,6],[3,5]]
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,2,3,6],[4,5]]
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,2,4,5],[3,6]]
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,3,5],[4,6]]
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,5,6],[2],[4]]
 => [1,2,3] => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,4,6],[2],[5]]
 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4,6],[3],[5]]
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,2,4,5],[3],[6]]
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,3,5],[4],[6]]
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,5],[2,4,6]]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,2,5],[3,4,6]]
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,3,4],[2,5,6]]
 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4],[3,5,6]]
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,2,3],[4,5,6]]
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,4,6],[2,5],[3]]
 => [1,1,2,2] => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,6],[2,5],[4]]
 => [1,2,3] => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,6],[2,4],[5]]
 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,6],[3,4],[5]]
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,3,5],[2,6],[4]]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,2,5],[3,6],[4]]
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,3,4],[2,6],[5]]
 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4],[3,6],[5]]
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,3,5],[2,4],[6]]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,2,5],[3,4],[6]]
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4],[3,5],[6]]
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,2,3],[4,5],[6]]
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,4,6],[2],[3],[5]]
 => [1,1,2,2] => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,6],[2],[4],[5]]
 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,3,5],[2],[4],[6]]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,2,5],[3],[4],[6]]
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4],[3],[5],[6]]
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,4],[2,5],[3,6]]
 => [1,1,2,2] => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3],[2,5],[4,6]]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,2],[3,5],[4,6]]
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,3],[2,4],[5,6]]
 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2],[3,4],[5,6]]
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,4],[2,6],[3],[5]]
 => [1,1,2,2] => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3],[2,6],[4],[5]]
 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,4],[2,5],[3],[6]]
 => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3],[2,5],[4],[6]]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,2],[3,5],[4],[6]]
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
Description
The number of 2-regular simple modules in the incidence algebra of the lattice.
Matching statistic: St001877
Mapping
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001877: Lattices ⟶ ℤResult quality: 85% ●values known / values provided: 85%●distinct values known / distinct values provided: 100%
Values
[[1,3,5],[2,4]]
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,2,4],[3,5]]
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,5],[2],[4]]
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,2,4],[3],[5]]
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3],[2,5],[4]]
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,2],[3,4],[5]]
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,2,3,5,6],[4]]
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,5,6],[2,4]]
 => [1,2,3] => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,4,6],[2,5]]
 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4,6],[3,5]]
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,2,3,6],[4,5]]
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,2,4,5],[3,6]]
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,3,5],[4,6]]
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,5,6],[2],[4]]
 => [1,2,3] => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,4,6],[2],[5]]
 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4,6],[3],[5]]
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,2,4,5],[3],[6]]
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,3,5],[4],[6]]
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,5],[2,4,6]]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,2,5],[3,4,6]]
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,3,4],[2,5,6]]
 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4],[3,5,6]]
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,2,3],[4,5,6]]
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,4,6],[2,5],[3]]
 => [1,1,2,2] => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,6],[2,5],[4]]
 => [1,2,3] => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,6],[2,4],[5]]
 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,6],[3,4],[5]]
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,3,5],[2,6],[4]]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,2,5],[3,6],[4]]
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,3,4],[2,6],[5]]
 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4],[3,6],[5]]
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,3,5],[2,4],[6]]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,2,5],[3,4],[6]]
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4],[3,5],[6]]
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,2,3],[4,5],[6]]
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,4,6],[2],[3],[5]]
 => [1,1,2,2] => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3,6],[2],[4],[5]]
 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,3,5],[2],[4],[6]]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,2,5],[3],[4],[6]]
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4],[3],[5],[6]]
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,4],[2,5],[3,6]]
 => [1,1,2,2] => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3],[2,5],[4,6]]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,2],[3,5],[4,6]]
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,3],[2,4],[5,6]]
 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2],[3,4],[5,6]]
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[[1,4],[2,6],[3],[5]]
 => [1,1,2,2] => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3],[2,6],[4],[5]]
 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,4],[2,5],[3],[6]]
 => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
 => ([(0,2),(2,1)],3)
 => 0
[[1,3],[2,5],[4],[6]]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
[[1,2],[3,5],[4],[6]]
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[[1,2,4,5,7,8],[3,6]]
 => [2,3,3] => [[6,4,2],[3,1]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,5,7,8],[4,6]]
 => [3,2,3] => [[6,4,3],[3,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,5,6,8],[4,7]]
 => [3,3,2] => [[6,5,3],[4,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,4,5,7,8],[3],[6]]
 => [2,3,3] => [[6,4,2],[3,1]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,5,7,8],[4],[6]]
 => [3,2,3] => [[6,4,3],[3,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,5,6,8],[4],[7]]
 => [3,3,2] => [[6,5,3],[4,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,5,7,8],[3,4,6]]
 => [2,3,3] => [[6,4,2],[3,1]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,6,8],[4,5,7]]
 => [3,3,2] => [[6,5,3],[4,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,4,5,8],[3,6,7]]
 => [2,3,3] => [[6,4,2],[3,1]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,5,8],[4,6,7]]
 => [3,2,3] => [[6,4,3],[3,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,5,6],[4,7,8]]
 => [3,3,2] => [[6,5,3],[4,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,5,7,8],[3,4],[6]]
 => [2,3,3] => [[6,4,2],[3,1]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,7,8],[4,5],[6]]
 => [3,2,3] => [[6,4,3],[3,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,4,5,8],[3,7],[6]]
 => [2,3,3] => [[6,4,2],[3,1]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,5,8],[4,7],[6]]
 => [3,2,3] => [[6,4,3],[3,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,6,8],[4,5],[7]]
 => [3,3,2] => [[6,5,3],[4,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,5,6],[4,8],[7]]
 => [3,3,2] => [[6,5,3],[4,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,6],[4,5,7,8]]
 => [3,3,2] => [[6,5,3],[4,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,4,5],[3,6,7,8]]
 => [2,3,3] => [[6,4,2],[3,1]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,5],[4,6,7,8]]
 => [3,2,3] => [[6,4,3],[3,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,5,8],[3,4,7],[6]]
 => [2,3,3] => [[6,4,2],[3,1]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,8],[4,5,7],[6]]
 => [3,2,3] => [[6,4,3],[3,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,8],[4,5,6],[7]]
 => [3,3,2] => [[6,5,3],[4,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,4,5],[3,7,8],[6]]
 => [2,3,3] => [[6,4,2],[3,1]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,5],[4,7,8],[6]]
 => [3,2,3] => [[6,4,3],[3,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,6],[4,5,8],[7]]
 => [3,3,2] => [[6,5,3],[4,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,5,8],[3,4],[6,7]]
 => [2,3,3] => [[6,4,2],[3,1]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,8],[4,5],[6,7]]
 => [3,2,3] => [[6,4,3],[3,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3,6],[4,5],[7,8]]
 => [3,3,2] => [[6,5,3],[4,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,5],[3,4,8],[6,7]]
 => [2,3,3] => [[6,4,2],[3,1]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3],[4,5,8],[6,7]]
 => [3,2,3] => [[6,4,3],[3,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,2,3],[4,5,6],[7,8]]
 => [3,3,2] => [[6,5,3],[4,2]]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 2
[[1,4,7],[2,5,8],[3],[6]]
 => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,4,6],[2,5,7],[3],[8]]
 => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,3,6],[2,4,7],[5],[8]]
 => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,4,7],[2,5],[3,8],[6]]
 => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,4,6],[2,5],[3,7],[8]]
 => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,3,6],[2,4],[5,7],[8]]
 => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,4,7],[2,8],[3],[5],[6]]
 => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,4,7],[2,5],[3],[6],[8]]
 => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,4,6],[2,7],[3],[5],[8]]
 => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,3,6],[2,7],[4],[5],[8]]
 => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,4,6],[2,5],[3],[7],[8]]
 => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,3,6],[2,4],[5],[7],[8]]
 => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,4,7],[2],[3],[5],[6],[8]]
 => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,4,6],[2],[3],[5],[7],[8]]
 => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,3,6],[2],[4],[5],[7],[8]]
 => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,4],[2,5],[3,7],[6,8]]
 => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,4],[2,7],[3,8],[5],[6]]
 => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
[[1,4],[2,6],[3,7],[5],[8]]
 => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2
Description
Number of indecomposable injective modules with projective dimension 2.
Matching statistic: St001330
Mapping
Mp00134: Standard tableaux —descent word⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 67%
Values
[[1,3,5],[2,4]]
 => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 0 + 4
[[1,2,4],[3,5]]
 => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 0 + 4
[[1,3,5],[2],[4]]
 => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 0 + 4
[[1,2,4],[3],[5]]
 => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 0 + 4
[[1,3],[2,5],[4]]
 => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 0 + 4
[[1,2],[3,4],[5]]
 => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 0 + 4
[[1,2,3,5,6],[4]]
 => 00100 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 4
[[1,3,5,6],[2,4]]
 => 10100 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 0 + 4
[[1,3,4,6],[2,5]]
 => 10010 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,2,4,6],[3,5]]
 => 01010 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 1 + 4
[[1,2,3,6],[4,5]]
 => 00100 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 4
[[1,2,4,5],[3,6]]
 => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,2,3,5],[4,6]]
 => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 4
[[1,3,5,6],[2],[4]]
 => 10100 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 0 + 4
[[1,3,4,6],[2],[5]]
 => 10010 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,2,4,6],[3],[5]]
 => 01010 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 1 + 4
[[1,2,4,5],[3],[6]]
 => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,2,3,5],[4],[6]]
 => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 4
[[1,3,5],[2,4,6]]
 => 10101 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 1 + 4
[[1,2,5],[3,4,6]]
 => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,3,4],[2,5,6]]
 => 10010 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,2,4],[3,5,6]]
 => 01010 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 1 + 4
[[1,2,3],[4,5,6]]
 => 00100 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 4
[[1,4,6],[2,5],[3]]
 => 11010 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 4
[[1,3,6],[2,5],[4]]
 => 10100 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 0 + 4
[[1,3,6],[2,4],[5]]
 => 10110 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,2,6],[3,4],[5]]
 => 01010 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 1 + 4
[[1,3,5],[2,6],[4]]
 => 10101 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 1 + 4
[[1,2,5],[3,6],[4]]
 => 01101 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,3,4],[2,6],[5]]
 => 10010 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,2,4],[3,6],[5]]
 => 01010 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 1 + 4
[[1,3,5],[2,4],[6]]
 => 10101 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 1 + 4
[[1,2,5],[3,4],[6]]
 => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,2,4],[3,5],[6]]
 => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 0 + 4
[[1,2,3],[4,5],[6]]
 => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 4
[[1,4,6],[2],[3],[5]]
 => 11010 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 4
[[1,3,6],[2],[4],[5]]
 => 10110 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,3,5],[2],[4],[6]]
 => 10101 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 1 + 4
[[1,2,5],[3],[4],[6]]
 => 01101 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,2,4],[3],[5],[6]]
 => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 0 + 4
[[1,4],[2,5],[3,6]]
 => 11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 4
[[1,3],[2,5],[4,6]]
 => 10101 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 1 + 4
[[1,2],[3,5],[4,6]]
 => 01101 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,3],[2,4],[5,6]]
 => 10110 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,2],[3,4],[5,6]]
 => 01010 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 1 + 4
[[1,4],[2,6],[3],[5]]
 => 11010 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 4
[[1,3],[2,6],[4],[5]]
 => 10110 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,4],[2,5],[3],[6]]
 => 11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 4
[[1,3],[2,5],[4],[6]]
 => 10101 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 1 + 4
[[1,2],[3,5],[4],[6]]
 => 01101 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 4
[[1,2],[3,4],[5],[6]]
 => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 0 + 4
[[1,4],[2],[3],[5],[6]]
 => 11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 4
[[1,2,3,5,6,7],[4]]
 => 001000 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 4
[[1,2,3,4,6,7],[5]]
 => 000100 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 4
[[1,3,5,6,7],[2,4]]
 => 101000 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4 = 0 + 4
[[1,3,4,6,7],[2,5]]
 => 100100 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 4
[[1,2,4,6,7],[3,5]]
 => 010100 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,2,3,6,7],[4,5]]
 => 001000 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 4
[[1,3,4,5,7],[2,6]]
 => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 4
[[1,2,4,5,7],[3,6]]
 => 010010 => [1,1,2,1,1] => ([(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)
 => ? = 1 + 4
[[1,2,3,5,7],[4,6]]
 => 001010 => [2,1,1,1,1] => ([(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)
 => ? = 1 + 4
[[1,2,3,4,7],[5,6]]
 => 000100 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 4
[[1,2,4,5,6],[3,7]]
 => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 4
[[1,2,3,5,6],[4,7]]
 => 001001 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 4
[[1,2,3,4,6],[5,7]]
 => 000101 => [3,1,1,1] => ([(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)
 => ? = 0 + 4
[[1,3,5,6,7],[2],[4]]
 => 101000 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4 = 0 + 4
[[1,3,4,6,7],[2],[5]]
 => 100100 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 4
[[1,2,4,6,7],[3],[5]]
 => 010100 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,2,3,6,7],[4],[5]]
 => 001100 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 4
[[1,3,4,5,7],[2],[6]]
 => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 4
[[1,2,4,5,7],[3],[6]]
 => 010010 => [1,1,2,1,1] => ([(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)
 => ? = 1 + 4
[[1,2,3,5,7],[4],[6]]
 => 001010 => [2,1,1,1,1] => ([(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)
 => ? = 1 + 4
[[1,2,4,5,6],[3],[7]]
 => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 4
[[1,2,3,5,6],[4],[7]]
 => 001001 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 4
[[1,2,3,4,6],[5],[7]]
 => 000101 => [3,1,1,1] => ([(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)
 => ? = 0 + 4
[[1,2,5,7],[3,4,6]]
 => 010010 => [1,1,2,1,1] => ([(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)
 => ? = 1 + 4
[[1,3,4,7],[2,5,6]]
 => 100100 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 4
[[1,2,4,7],[3,5,6]]
 => 010100 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,2,3,7],[4,5,6]]
 => 001000 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 4
[[1,3,6,7],[2,5],[4]]
 => 101000 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4 = 0 + 4
[[1,2,6,7],[3,4],[5]]
 => 010100 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,2,4,7],[3,6],[5]]
 => 010100 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,2,4],[3,6,7],[5]]
 => 010100 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,3,5],[2,4,6],[7]]
 => 101011 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,2,7],[3,4],[5,6]]
 => 010100 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,3,5],[2,6],[4],[7]]
 => 101011 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,3,5],[2,4],[6],[7]]
 => 101011 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,2,4],[3,5],[6],[7]]
 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4 = 0 + 4
[[1,3,5],[2],[4],[6],[7]]
 => 101011 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,2,4],[3],[5],[6],[7]]
 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4 = 0 + 4
[[1,3],[2,5],[4,6],[7]]
 => 101011 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,3],[2,5],[4],[6],[7]]
 => 101011 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 1 + 4
[[1,2],[3,4],[5],[6],[7]]
 => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4 = 0 + 4
Description
The hat guessing number of a graph. Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors. Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.