Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001421
(load all 4 compositions to match this statistic)
Mapping
St001421: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0
1 => 0
00 => 0
01 => 0
10 => 1
11 => 0
000 => 0
001 => 0
010 => 1
011 => 0
100 => 1
101 => 1
110 => 1
111 => 0
0000 => 0
0001 => 0
0010 => 1
0011 => 0
0100 => 1
0101 => 1
0110 => 1
0111 => 0
1000 => 1
1001 => 1
1010 => 2
1011 => 1
1100 => 2
1101 => 1
1110 => 1
1111 => 0
00000 => 0
00001 => 0
00010 => 1
00011 => 0
00100 => 1
00101 => 1
00110 => 1
00111 => 0
01000 => 1
01001 => 1
01010 => 2
01011 => 1
01100 => 2
01101 => 1
01110 => 1
01111 => 0
10000 => 1
10001 => 1
10010 => 1
10011 => 1
Description
Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word.
Matching statistic: St000259
Mapping
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 60% ●values known / values provided: 66%●distinct values known / distinct values provided: 60%
Values
0 => [1] => [1] => ([],1)
 => 0
1 => [1] => [1] => ([],1)
 => 0
00 => [2] => [1] => ([],1)
 => 0
01 => [1,1] => [2] => ([],2)
 => ? ∊ {0,1}
10 => [1,1] => [2] => ([],2)
 => ? ∊ {0,1}
11 => [2] => [1] => ([],1)
 => 0
000 => [3] => [1] => ([],1)
 => 0
001 => [2,1] => [1,1] => ([(0,1)],2)
 => 1
010 => [1,1,1] => [3] => ([],3)
 => ? ∊ {0,0}
011 => [1,2] => [1,1] => ([(0,1)],2)
 => 1
100 => [1,2] => [1,1] => ([(0,1)],2)
 => 1
101 => [1,1,1] => [3] => ([],3)
 => ? ∊ {0,0}
110 => [2,1] => [1,1] => ([(0,1)],2)
 => 1
111 => [3] => [1] => ([],1)
 => 0
0000 => [4] => [1] => ([],1)
 => 0
0001 => [3,1] => [1,1] => ([(0,1)],2)
 => 1
0010 => [2,1,1] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,0,1,1,1}
0011 => [2,2] => [2] => ([],2)
 => ? ∊ {0,0,0,1,1,1}
0100 => [1,1,2] => [2,1] => ([(0,2),(1,2)],3)
 => 2
0101 => [1,1,1,1] => [4] => ([],4)
 => ? ∊ {0,0,0,1,1,1}
0110 => [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
0111 => [1,3] => [1,1] => ([(0,1)],2)
 => 1
1000 => [1,3] => [1,1] => ([(0,1)],2)
 => 1
1001 => [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
1010 => [1,1,1,1] => [4] => ([],4)
 => ? ∊ {0,0,0,1,1,1}
1011 => [1,1,2] => [2,1] => ([(0,2),(1,2)],3)
 => 2
1100 => [2,2] => [2] => ([],2)
 => ? ∊ {0,0,0,1,1,1}
1101 => [2,1,1] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,0,1,1,1}
1110 => [3,1] => [1,1] => ([(0,1)],2)
 => 1
1111 => [4] => [1] => ([],1)
 => 0
00000 => [5] => [1] => ([],1)
 => 0
00001 => [4,1] => [1,1] => ([(0,1)],2)
 => 1
00010 => [3,1,1] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
00011 => [3,2] => [1,1] => ([(0,1)],2)
 => 1
00100 => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
00101 => [2,1,1,1] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
00110 => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 2
00111 => [2,3] => [1,1] => ([(0,1)],2)
 => 1
01000 => [1,1,3] => [2,1] => ([(0,2),(1,2)],3)
 => 2
01001 => [1,1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
01010 => [1,1,1,1,1] => [5] => ([],5)
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
01011 => [1,1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
01100 => [1,2,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
01101 => [1,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
01110 => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
01111 => [1,4] => [1,1] => ([(0,1)],2)
 => 1
10000 => [1,4] => [1,1] => ([(0,1)],2)
 => 1
10001 => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
10010 => [1,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
10011 => [1,2,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
10100 => [1,1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
10101 => [1,1,1,1,1] => [5] => ([],5)
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
10110 => [1,1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
10111 => [1,1,3] => [2,1] => ([(0,2),(1,2)],3)
 => 2
11000 => [2,3] => [1,1] => ([(0,1)],2)
 => 1
11001 => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 2
11010 => [2,1,1,1] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
11011 => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
11100 => [3,2] => [1,1] => ([(0,1)],2)
 => 1
11101 => [3,1,1] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
11110 => [4,1] => [1,1] => ([(0,1)],2)
 => 1
11111 => [5] => [1] => ([],1)
 => 0
000000 => [6] => [1] => ([],1)
 => 0
000001 => [5,1] => [1,1] => ([(0,1)],2)
 => 1
000010 => [4,1,1] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
000011 => [4,2] => [1,1] => ([(0,1)],2)
 => 1
000100 => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
000101 => [3,1,1,1] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
000110 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
000111 => [3,3] => [2] => ([],2)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
001000 => [2,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
001001 => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
001010 => [2,1,1,1,1] => [1,4] => ([(3,4)],5)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
001011 => [2,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
001100 => [2,2,2] => [3] => ([],3)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
001101 => [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
010010 => [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
010011 => [1,1,2,2] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
010101 => [1,1,1,1,1,1] => [6] => ([],6)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
011010 => [1,2,1,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
011101 => [1,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
100010 => [1,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
100101 => [1,2,1,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
101010 => [1,1,1,1,1,1] => [6] => ([],6)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
101100 => [1,1,2,2] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
101101 => [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
110010 => [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
110011 => [2,2,2] => [3] => ([],3)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
110101 => [2,1,1,1,1] => [1,4] => ([(3,4)],5)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
111000 => [3,3] => [2] => ([],2)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
111010 => [3,1,1,1] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
111101 => [4,1,1] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3}
0000010 => [5,1,1] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
0000101 => [4,1,1,1] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
0001010 => [3,1,1,1,1] => [1,4] => ([(3,4)],5)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
0001100 => [3,2,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
0001101 => [3,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
0010010 => [2,1,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
0010011 => [2,1,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
0010101 => [2,1,1,1,1,1] => [1,5] => ([(4,5)],6)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St001878
(load all 2 compositions to match this statistic)
Mapping
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 19% ●values known / values provided: 19%●distinct values known / distinct values provided: 40%
Values
0 => [1] => [[1],[]]
 => ([],1)
 => ? ∊ {0,0}
1 => [1] => [[1],[]]
 => ([],1)
 => ? ∊ {0,0}
00 => [2] => [[2],[]]
 => ([],1)
 => ? ∊ {0,0,0,1}
01 => [1,1] => [[1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,1}
10 => [1,1] => [[1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,1}
11 => [2] => [[2],[]]
 => ([],1)
 => ? ∊ {0,0,0,1}
000 => [3] => [[3],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,1,1,1,1}
001 => [2,1] => [[2,2],[1]]
 => ([],1)
 => ? ∊ {0,0,0,0,1,1,1,1}
010 => [1,1,1] => [[1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,1,1,1,1}
011 => [1,2] => [[2,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,1,1,1,1}
100 => [1,2] => [[2,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,1,1,1,1}
101 => [1,1,1] => [[1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,1,1,1,1}
110 => [2,1] => [[2,2],[1]]
 => ([],1)
 => ? ∊ {0,0,0,0,1,1,1,1}
111 => [3] => [[3],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,1,1,1,1}
0000 => [4] => [[4],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
0001 => [3,1] => [[3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
0010 => [2,1,1] => [[2,2,2],[1,1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
0011 => [2,2] => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
0100 => [1,1,2] => [[2,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
0101 => [1,1,1,1] => [[1,1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
0110 => [1,2,1] => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
0111 => [1,3] => [[3,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
1000 => [1,3] => [[3,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
1001 => [1,2,1] => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
1010 => [1,1,1,1] => [[1,1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
1011 => [1,1,2] => [[2,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
1100 => [2,2] => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
1101 => [2,1,1] => [[2,2,2],[1,1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
1110 => [3,1] => [[3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
1111 => [4] => [[4],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2}
00000 => [5] => [[5],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
00001 => [4,1] => [[4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
00010 => [3,1,1] => [[3,3,3],[2,2]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
00011 => [3,2] => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
00100 => [2,1,2] => [[3,2,2],[1,1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
00101 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
00110 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
00111 => [2,3] => [[4,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
01000 => [1,1,3] => [[3,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
01001 => [1,1,2,1] => [[2,2,1,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
01010 => [1,1,1,1,1] => [[1,1,1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
01011 => [1,1,1,2] => [[2,1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
01100 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
01101 => [1,2,1,1] => [[2,2,2,1],[1,1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
01110 => [1,3,1] => [[3,3,1],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
01111 => [1,4] => [[4,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
10000 => [1,4] => [[4,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
10001 => [1,3,1] => [[3,3,1],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
10010 => [1,2,1,1] => [[2,2,2,1],[1,1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
10011 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
10100 => [1,1,1,2] => [[2,1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
10101 => [1,1,1,1,1] => [[1,1,1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
10110 => [1,1,2,1] => [[2,2,1,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
11001 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 1
000110 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
000111 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
001001 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
001100 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
001101 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 1
001110 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
010010 => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
 => ([(0,2),(2,1)],3)
 => 1
010011 => [1,1,2,2] => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
011000 => [1,2,3] => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
011001 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
011011 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
011100 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
100011 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
100100 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
100110 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
100111 => [1,2,3] => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
101100 => [1,1,2,2] => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 1
101101 => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
 => ([(0,2),(2,1)],3)
 => 1
110001 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
110010 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 1
110011 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
110110 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
111000 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
111001 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 1
0000110 => [4,2,1] => [[5,5,4],[4,3]]
 => ([(0,2),(2,1)],3)
 => 1
0000111 => [4,3] => [[6,4],[3]]
 => ([(0,2),(2,1)],3)
 => 1
0001000 => [3,1,3] => [[5,3,3],[2,2]]
 => ([(0,2),(2,1)],3)
 => 1
0001001 => [3,1,2,1] => [[4,4,3,3],[3,2,2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
0001100 => [3,2,2] => [[5,4,3],[3,2]]
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 2
0001101 => [3,2,1,1] => [[4,4,4,3],[3,3,2]]
 => ([(0,2),(2,1)],3)
 => 1
0001110 => [3,3,1] => [[5,5,3],[4,2]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
0001111 => [3,4] => [[6,3],[2]]
 => ([(0,2),(2,1)],3)
 => 1
0010001 => [2,1,3,1] => [[4,4,2,2],[3,1,1]]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 2
0010010 => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
0010011 => [2,1,2,2] => [[4,3,2,2],[2,1,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => 2
0010110 => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
0011000 => [2,2,3] => [[5,3,2],[2,1]]
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 2
0011001 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => 1
0011010 => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]]
 => ([(0,2),(2,1)],3)
 => 1
0011011 => [2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => 2
0011100 => [2,3,2] => [[5,4,2],[3,1]]
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 2
0011101 => [2,3,1,1] => [[4,4,4,2],[3,3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
0011110 => [2,4,1] => [[5,5,2],[4,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
0100010 => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]]
 => ([(0,2),(2,1)],3)
 => 1
0100011 => [1,1,3,2] => [[4,3,1,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
0100100 => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.