Your data matches 74 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000288
(load all 19 compositions to match this statistic)
Mapping
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
St000288: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 => 1 = 2 - 1
1 => 1 => 1 = 2 - 1
00 => 01 => 1 = 2 - 1
01 => 10 => 1 = 2 - 1
10 => 11 => 2 = 3 - 1
11 => 11 => 2 = 3 - 1
000 => 001 => 1 = 2 - 1
001 => 010 => 1 = 2 - 1
101 => 110 => 2 = 3 - 1
110 => 111 => 3 = 4 - 1
111 => 111 => 3 = 4 - 1
0000 => 0001 => 1 = 2 - 1
0001 => 0010 => 1 = 2 - 1
1101 => 1110 => 3 = 4 - 1
1110 => 1111 => 4 = 5 - 1
1111 => 1111 => 4 = 5 - 1
00000 => 00001 => 1 = 2 - 1
00001 => 00010 => 1 = 2 - 1
11101 => 11110 => 4 = 5 - 1
11110 => 11111 => 5 = 6 - 1
11111 => 11111 => 5 = 6 - 1
000000 => 000001 => 1 = 2 - 1
111101 => 111110 => 5 = 6 - 1
111110 => 111111 => 6 = 7 - 1
111111 => 111111 => 6 = 7 - 1
0000000 => 0000001 => 1 = 2 - 1
1111110 => 1111111 => 7 = 8 - 1
1111111 => 1111111 => 7 = 8 - 1
Description
The number of ones in a binary word. This is also known as the Hamming weight of the word.
Matching statistic: St000392
(load all 9 compositions to match this statistic)
Mapping
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
St000392: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 => 1 = 2 - 1
1 => 1 => 1 = 2 - 1
00 => 01 => 1 = 2 - 1
01 => 10 => 1 = 2 - 1
10 => 11 => 2 = 3 - 1
11 => 11 => 2 = 3 - 1
000 => 001 => 1 = 2 - 1
001 => 010 => 1 = 2 - 1
101 => 110 => 2 = 3 - 1
110 => 111 => 3 = 4 - 1
111 => 111 => 3 = 4 - 1
0000 => 0001 => 1 = 2 - 1
0001 => 0010 => 1 = 2 - 1
1101 => 1110 => 3 = 4 - 1
1110 => 1111 => 4 = 5 - 1
1111 => 1111 => 4 = 5 - 1
00000 => 00001 => 1 = 2 - 1
00001 => 00010 => 1 = 2 - 1
11101 => 11110 => 4 = 5 - 1
11110 => 11111 => 5 = 6 - 1
11111 => 11111 => 5 = 6 - 1
000000 => 000001 => 1 = 2 - 1
111101 => 111110 => 5 = 6 - 1
111110 => 111111 => 6 = 7 - 1
111111 => 111111 => 6 = 7 - 1
0000000 => 0000001 => 1 = 2 - 1
1111110 => 1111111 => 7 = 8 - 1
1111111 => 1111111 => 7 = 8 - 1
Description
The length of the longest run of ones in a binary word.
Matching statistic: St001372
(load all 17 compositions to match this statistic)
Mapping
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
St001372: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 => 1 = 2 - 1
1 => 1 => 1 = 2 - 1
00 => 01 => 1 = 2 - 1
01 => 10 => 1 = 2 - 1
10 => 11 => 2 = 3 - 1
11 => 11 => 2 = 3 - 1
000 => 001 => 1 = 2 - 1
001 => 010 => 1 = 2 - 1
101 => 110 => 2 = 3 - 1
110 => 111 => 3 = 4 - 1
111 => 111 => 3 = 4 - 1
0000 => 0001 => 1 = 2 - 1
0001 => 0010 => 1 = 2 - 1
1101 => 1110 => 3 = 4 - 1
1110 => 1111 => 4 = 5 - 1
1111 => 1111 => 4 = 5 - 1
00000 => 00001 => 1 = 2 - 1
00001 => 00010 => 1 = 2 - 1
11101 => 11110 => 4 = 5 - 1
11110 => 11111 => 5 = 6 - 1
11111 => 11111 => 5 = 6 - 1
000000 => 000001 => 1 = 2 - 1
111101 => 111110 => 5 = 6 - 1
111110 => 111111 => 6 = 7 - 1
111111 => 111111 => 6 = 7 - 1
0000000 => 0000001 => 1 = 2 - 1
1111110 => 1111111 => 7 = 8 - 1
1111111 => 1111111 => 7 = 8 - 1
Description
The length of a longest cyclic run of ones of a binary word. Consider the binary word as a cyclic arrangement of ones and zeros. Then this statistic is the length of the longest continuous sequence of ones in this arrangement.
Matching statistic: St001419
(load all 9 compositions to match this statistic)
Mapping
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
St001419: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 => 1 = 2 - 1
1 => 1 => 1 = 2 - 1
00 => 01 => 1 = 2 - 1
01 => 10 => 1 = 2 - 1
10 => 11 => 2 = 3 - 1
11 => 11 => 2 = 3 - 1
000 => 001 => 1 = 2 - 1
001 => 010 => 1 = 2 - 1
101 => 110 => 2 = 3 - 1
110 => 111 => 3 = 4 - 1
111 => 111 => 3 = 4 - 1
0000 => 0001 => 1 = 2 - 1
0001 => 0010 => 1 = 2 - 1
1101 => 1110 => 3 = 4 - 1
1110 => 1111 => 4 = 5 - 1
1111 => 1111 => 4 = 5 - 1
00000 => 00001 => 1 = 2 - 1
00001 => 00010 => 1 = 2 - 1
11101 => 11110 => 4 = 5 - 1
11110 => 11111 => 5 = 6 - 1
11111 => 11111 => 5 = 6 - 1
000000 => 000001 => 1 = 2 - 1
111101 => 111110 => 5 = 6 - 1
111110 => 111111 => 6 = 7 - 1
111111 => 111111 => 6 = 7 - 1
0000000 => 0000001 => 1 = 2 - 1
1111110 => 1111111 => 7 = 8 - 1
1111111 => 1111111 => 7 = 8 - 1
Description
The length of the longest palindromic factor beginning with a one of a binary word.
Matching statistic: St000297
Mapping
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
Mp00261: Binary words —Burrows-Wheeler⟶ Binary words
St000297: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 => 1 => 1 = 2 - 1
1 => 1 => 1 => 1 = 2 - 1
00 => 01 => 10 => 1 = 2 - 1
01 => 10 => 10 => 1 = 2 - 1
10 => 11 => 11 => 2 = 3 - 1
11 => 11 => 11 => 2 = 3 - 1
000 => 001 => 100 => 1 = 2 - 1
001 => 010 => 100 => 1 = 2 - 1
101 => 110 => 110 => 2 = 3 - 1
110 => 111 => 111 => 3 = 4 - 1
111 => 111 => 111 => 3 = 4 - 1
0000 => 0001 => 1000 => 1 = 2 - 1
0001 => 0010 => 1000 => 1 = 2 - 1
1101 => 1110 => 1110 => 3 = 4 - 1
1110 => 1111 => 1111 => 4 = 5 - 1
1111 => 1111 => 1111 => 4 = 5 - 1
00000 => 00001 => 10000 => 1 = 2 - 1
00001 => 00010 => 10000 => 1 = 2 - 1
11101 => 11110 => 11110 => 4 = 5 - 1
11110 => 11111 => 11111 => 5 = 6 - 1
11111 => 11111 => 11111 => 5 = 6 - 1
000000 => 000001 => 100000 => 1 = 2 - 1
111101 => 111110 => 111110 => 5 = 6 - 1
111110 => 111111 => 111111 => 6 = 7 - 1
111111 => 111111 => 111111 => 6 = 7 - 1
0000000 => 0000001 => 1000000 => 1 = 2 - 1
1111110 => 1111111 => 1111111 => 7 = 8 - 1
1111111 => 1111111 => 1111111 => 7 = 8 - 1
Description
The number of leading ones in a binary word.
Matching statistic: St000982
(load all 6 compositions to match this statistic)
Mapping
Mp00104: Binary words —reverse⟶ Binary words
Mp00268: Binary words —zeros to flag zeros⟶ Binary words
St000982: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 => 0 => 1 = 2 - 1
1 => 1 => 1 => 1 = 2 - 1
00 => 00 => 10 => 1 = 2 - 1
01 => 10 => 01 => 1 = 2 - 1
10 => 01 => 00 => 2 = 3 - 1
11 => 11 => 11 => 2 = 3 - 1
000 => 000 => 010 => 1 = 2 - 1
001 => 100 => 101 => 1 = 2 - 1
101 => 101 => 001 => 2 = 3 - 1
110 => 011 => 000 => 3 = 4 - 1
111 => 111 => 111 => 3 = 4 - 1
0000 => 0000 => 1010 => 1 = 2 - 1
0001 => 1000 => 0101 => 1 = 2 - 1
1101 => 1011 => 0001 => 3 = 4 - 1
1110 => 0111 => 0000 => 4 = 5 - 1
1111 => 1111 => 1111 => 4 = 5 - 1
00000 => 00000 => 01010 => 1 = 2 - 1
00001 => 10000 => 10101 => 1 = 2 - 1
11101 => 10111 => 00001 => 4 = 5 - 1
11110 => 01111 => 00000 => 5 = 6 - 1
11111 => 11111 => 11111 => 5 = 6 - 1
000000 => 000000 => 101010 => 1 = 2 - 1
111101 => 101111 => 000001 => 5 = 6 - 1
111110 => 011111 => 000000 => 6 = 7 - 1
111111 => 111111 => 111111 => 6 = 7 - 1
0000000 => 0000000 => 0101010 => 1 = 2 - 1
1111110 => 0111111 => 0000000 => 7 = 8 - 1
1111111 => 1111111 => 1111111 => 7 = 8 - 1
Description
The length of the longest constant subword.
Matching statistic: St001415
(load all 4 compositions to match this statistic)
Mapping
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
Mp00261: Binary words —Burrows-Wheeler⟶ Binary words
St001415: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 => 1 => 1 = 2 - 1
1 => 1 => 1 => 1 = 2 - 1
00 => 01 => 10 => 1 = 2 - 1
01 => 10 => 10 => 1 = 2 - 1
10 => 11 => 11 => 2 = 3 - 1
11 => 11 => 11 => 2 = 3 - 1
000 => 001 => 100 => 1 = 2 - 1
001 => 010 => 100 => 1 = 2 - 1
101 => 110 => 110 => 2 = 3 - 1
110 => 111 => 111 => 3 = 4 - 1
111 => 111 => 111 => 3 = 4 - 1
0000 => 0001 => 1000 => 1 = 2 - 1
0001 => 0010 => 1000 => 1 = 2 - 1
1101 => 1110 => 1110 => 3 = 4 - 1
1110 => 1111 => 1111 => 4 = 5 - 1
1111 => 1111 => 1111 => 4 = 5 - 1
00000 => 00001 => 10000 => 1 = 2 - 1
00001 => 00010 => 10000 => 1 = 2 - 1
11101 => 11110 => 11110 => 4 = 5 - 1
11110 => 11111 => 11111 => 5 = 6 - 1
11111 => 11111 => 11111 => 5 = 6 - 1
000000 => 000001 => 100000 => 1 = 2 - 1
111101 => 111110 => 111110 => 5 = 6 - 1
111110 => 111111 => 111111 => 6 = 7 - 1
111111 => 111111 => 111111 => 6 = 7 - 1
0000000 => 0000001 => 1000000 => 1 = 2 - 1
1111110 => 1111111 => 1111111 => 7 = 8 - 1
1111111 => 1111111 => 1111111 => 7 = 8 - 1
Description
The length of the longest palindromic prefix of a binary word.
Matching statistic: St000010
Mapping
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000010: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 => [1,1] => [1,1]
 => 2
1 => 1 => [1,1] => [1,1]
 => 2
00 => 01 => [2,1] => [2,1]
 => 2
01 => 10 => [1,2] => [2,1]
 => 2
10 => 11 => [1,1,1] => [1,1,1]
 => 3
11 => 11 => [1,1,1] => [1,1,1]
 => 3
000 => 001 => [3,1] => [3,1]
 => 2
001 => 010 => [2,2] => [2,2]
 => 2
101 => 110 => [1,1,2] => [2,1,1]
 => 3
110 => 111 => [1,1,1,1] => [1,1,1,1]
 => 4
111 => 111 => [1,1,1,1] => [1,1,1,1]
 => 4
0000 => 0001 => [4,1] => [4,1]
 => 2
0001 => 0010 => [3,2] => [3,2]
 => 2
1101 => 1110 => [1,1,1,2] => [2,1,1,1]
 => 4
1110 => 1111 => [1,1,1,1,1] => [1,1,1,1,1]
 => 5
1111 => 1111 => [1,1,1,1,1] => [1,1,1,1,1]
 => 5
00000 => 00001 => [5,1] => [5,1]
 => 2
00001 => 00010 => [4,2] => [4,2]
 => 2
11101 => 11110 => [1,1,1,1,2] => [2,1,1,1,1]
 => 5
11110 => 11111 => [1,1,1,1,1,1] => [1,1,1,1,1,1]
 => 6
11111 => 11111 => [1,1,1,1,1,1] => [1,1,1,1,1,1]
 => 6
000000 => 000001 => [6,1] => [6,1]
 => 2
111101 => 111110 => [1,1,1,1,1,2] => [2,1,1,1,1,1]
 => 6
111110 => 111111 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1]
 => 7
111111 => 111111 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1]
 => 7
0000000 => 0000001 => [7,1] => [7,1]
 => 2
1111110 => 1111111 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1]
 => 8
1111111 => 1111111 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1]
 => 8
Description
The length of the partition.
Matching statistic: St000097
Mapping
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000097: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 => [1,1] => ([(0,1)],2)
 => 2
1 => 1 => [1,1] => ([(0,1)],2)
 => 2
00 => 01 => [2,1] => ([(0,2),(1,2)],3)
 => 2
01 => 10 => [1,2] => ([(1,2)],3)
 => 2
10 => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
11 => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
000 => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
001 => 010 => [2,2] => ([(1,3),(2,3)],4)
 => 2
101 => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3
110 => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
111 => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
0000 => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
0001 => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 2
1101 => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
1110 => 1111 => [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
1111 => 1111 => [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
00000 => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
00001 => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 2
11101 => 11110 => [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
11110 => 11111 => [1,1,1,1,1,1] => ([(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
11111 => 11111 => [1,1,1,1,1,1] => ([(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
000000 => 000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
111101 => 111110 => [1,1,1,1,1,2] => ([(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)
 => 6
111110 => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(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)
 => 7
111111 => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(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)
 => 7
0000000 => 0000001 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => 2
1111110 => 1111111 => [1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => 8
1111111 => 1111111 => [1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => 8
Description
The order of the largest clique of the graph. A clique in a graph $G$ is a subset $U \subseteq V(G)$ such that any pair of vertices in $U$ are adjacent. I.e. the subgraph induced by $U$ is a complete graph.
Matching statistic: St000098
Mapping
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000098: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 => [1,1] => ([(0,1)],2)
 => 2
1 => 1 => [1,1] => ([(0,1)],2)
 => 2
00 => 01 => [2,1] => ([(0,2),(1,2)],3)
 => 2
01 => 10 => [1,2] => ([(1,2)],3)
 => 2
10 => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
11 => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
000 => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
001 => 010 => [2,2] => ([(1,3),(2,3)],4)
 => 2
101 => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3
110 => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
111 => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
0000 => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
0001 => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 2
1101 => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
1110 => 1111 => [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
1111 => 1111 => [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
00000 => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
00001 => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 2
11101 => 11110 => [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
11110 => 11111 => [1,1,1,1,1,1] => ([(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
11111 => 11111 => [1,1,1,1,1,1] => ([(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
000000 => 000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
111101 => 111110 => [1,1,1,1,1,2] => ([(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)
 => 6
111110 => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(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)
 => 7
111111 => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(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)
 => 7
0000000 => 0000001 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => 2
1111110 => 1111111 => [1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => 8
1111111 => 1111111 => [1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => 8
Description
The chromatic number of a graph. The minimal number of colors needed to color the vertices of the graph such that no two vertices which share an edge have the same color.
The following 64 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000326The position of the first one in a binary word after appending a 1 at the end. St000381The largest part of an integer composition. St000808The number of up steps of the associated bargraph. St001330The hat guessing number of a graph. St000382The first part of an integer composition. St000626The minimal period of a binary word. St000806The semiperimeter of the associated bargraph. St000877The depth of the binary word interpreted as a path. St000983The length of the longest alternating subword. St001313The number of Dyck paths above the lattice path given by a binary word. St000682The Grundy value of Welter's game on a binary word. St000691The number of changes of a binary word. St001581The achromatic number of a graph. St000172The Grundy number of a graph. St000918The 2-limited packing number of a graph. St001029The size of the core of a graph. St001116The game chromatic number of a graph. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001670The connected partition number of a graph. St000272The treewidth of a graph. St000362The size of a minimal vertex cover of a graph. St000482The (zero)-forcing number of a graph. St000536The pathwidth of a graph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001315The dissociation number of a graph. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001458The rank of the adjacency matrix of a graph. St001963The tree-depth of a graph. St001277The degeneracy of a graph. St001358The largest degree of a regular subgraph of a graph. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001235The global dimension of the corresponding Comp-Nakayama algebra. St000822The Hadwiger number of the graph. St001498The normalised height of a Nakayama algebra with magnitude 1. St001812The biclique partition number of a graph. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001557The number of inversions of the second entry of a permutation. St000260The radius of a connected graph. St000264The girth of a graph, which is not a tree. St001060The distinguishing index of a graph. St000284The Plancherel distribution on integer partitions. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000706The product of the factorials of the multiplicities of an integer partition. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000993The multiplicity of the largest part of an integer partition. St001128The exponens consonantiae of a partition. St001568The smallest positive integer that does not appear twice in the partition. St000567The sum of the products of all pairs of parts. St000929The constant term of the character polynomial of an integer partition. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001098The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for vertex labelled trees. St001099The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled binary trees. St001100The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled trees. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition.