Your data matches 7 different statistics following compositions of up to 3 maps.
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Matching statistic: St000982
(load all 3 compositions to match this statistic)
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
St000982: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [2] => 10 => 01 => 1
1 => [1,1] => 11 => 00 => 2
00 => [3] => 100 => 011 => 2
01 => [2,1] => 101 => 010 => 1
10 => [1,2] => 110 => 001 => 2
11 => [1,1,1] => 111 => 000 => 3
000 => [4] => 1000 => 0111 => 3
001 => [3,1] => 1001 => 0110 => 2
010 => [2,2] => 1010 => 0101 => 1
011 => [2,1,1] => 1011 => 0100 => 2
100 => [1,3] => 1100 => 0011 => 2
101 => [1,2,1] => 1101 => 0010 => 2
110 => [1,1,2] => 1110 => 0001 => 3
111 => [1,1,1,1] => 1111 => 0000 => 4
0000 => [5] => 10000 => 01111 => 4
0001 => [4,1] => 10001 => 01110 => 3
0010 => [3,2] => 10010 => 01101 => 2
0011 => [3,1,1] => 10011 => 01100 => 2
0100 => [2,3] => 10100 => 01011 => 2
0101 => [2,2,1] => 10101 => 01010 => 1
0110 => [2,1,2] => 10110 => 01001 => 2
0111 => [2,1,1,1] => 10111 => 01000 => 3
1000 => [1,4] => 11000 => 00111 => 3
1001 => [1,3,1] => 11001 => 00110 => 2
1010 => [1,2,2] => 11010 => 00101 => 2
1011 => [1,2,1,1] => 11011 => 00100 => 2
1100 => [1,1,3] => 11100 => 00011 => 3
1101 => [1,1,2,1] => 11101 => 00010 => 3
1110 => [1,1,1,2] => 11110 => 00001 => 4
1111 => [1,1,1,1,1] => 11111 => 00000 => 5
00000 => [6] => 100000 => 011111 => 5
00001 => [5,1] => 100001 => 011110 => 4
00010 => [4,2] => 100010 => 011101 => 3
00011 => [4,1,1] => 100011 => 011100 => 3
00100 => [3,3] => 100100 => 011011 => 2
00101 => [3,2,1] => 100101 => 011010 => 2
00110 => [3,1,2] => 100110 => 011001 => 2
00111 => [3,1,1,1] => 100111 => 011000 => 3
01000 => [2,4] => 101000 => 010111 => 3
01001 => [2,3,1] => 101001 => 010110 => 2
01010 => [2,2,2] => 101010 => 010101 => 1
01011 => [2,2,1,1] => 101011 => 010100 => 2
01100 => [2,1,3] => 101100 => 010011 => 2
01101 => [2,1,2,1] => 101101 => 010010 => 2
01110 => [2,1,1,2] => 101110 => 010001 => 3
01111 => [2,1,1,1,1] => 101111 => 010000 => 4
10000 => [1,5] => 110000 => 001111 => 4
10001 => [1,4,1] => 110001 => 001110 => 3
10010 => [1,3,2] => 110010 => 001101 => 2
10011 => [1,3,1,1] => 110011 => 001100 => 2
Description
The length of the longest constant subword.
Matching statistic: St000392
(load all 2 compositions to match this statistic)
Mapping
Mp00104: Binary words —reverse⟶ Binary words
Mp00269: Binary words —flag zeros to zeros⟶ Binary words
St000392: Binary words ⟶ ℤResult quality: 96% ●values known / values provided: 96%●distinct values known / distinct values provided: 100%
Values
0 => 0 => 0 => 0 = 1 - 1
1 => 1 => 1 => 1 = 2 - 1
00 => 00 => 01 => 1 = 2 - 1
01 => 10 => 00 => 0 = 1 - 1
10 => 01 => 10 => 1 = 2 - 1
11 => 11 => 11 => 2 = 3 - 1
000 => 000 => 011 => 2 = 3 - 1
001 => 100 => 010 => 1 = 2 - 1
010 => 010 => 000 => 0 = 1 - 1
011 => 110 => 001 => 1 = 2 - 1
100 => 001 => 101 => 1 = 2 - 1
101 => 101 => 100 => 1 = 2 - 1
110 => 011 => 110 => 2 = 3 - 1
111 => 111 => 111 => 3 = 4 - 1
0000 => 0000 => 0111 => 3 = 4 - 1
0001 => 1000 => 0110 => 2 = 3 - 1
0010 => 0100 => 0100 => 1 = 2 - 1
0011 => 1100 => 0101 => 1 = 2 - 1
0100 => 0010 => 0001 => 1 = 2 - 1
0101 => 1010 => 0000 => 0 = 1 - 1
0110 => 0110 => 0010 => 1 = 2 - 1
0111 => 1110 => 0011 => 2 = 3 - 1
1000 => 0001 => 1011 => 2 = 3 - 1
1001 => 1001 => 1010 => 1 = 2 - 1
1010 => 0101 => 1000 => 1 = 2 - 1
1011 => 1101 => 1001 => 1 = 2 - 1
1100 => 0011 => 1101 => 2 = 3 - 1
1101 => 1011 => 1100 => 2 = 3 - 1
1110 => 0111 => 1110 => 3 = 4 - 1
1111 => 1111 => 1111 => 4 = 5 - 1
00000 => 00000 => 01111 => 4 = 5 - 1
00001 => 10000 => 01110 => 3 = 4 - 1
00010 => 01000 => 01100 => 2 = 3 - 1
00011 => 11000 => 01101 => 2 = 3 - 1
00100 => 00100 => 01001 => 1 = 2 - 1
00101 => 10100 => 01000 => 1 = 2 - 1
00110 => 01100 => 01010 => 1 = 2 - 1
00111 => 11100 => 01011 => 2 = 3 - 1
01000 => 00010 => 00011 => 2 = 3 - 1
01001 => 10010 => 00010 => 1 = 2 - 1
01010 => 01010 => 00000 => 0 = 1 - 1
01011 => 11010 => 00001 => 1 = 2 - 1
01100 => 00110 => 00101 => 1 = 2 - 1
01101 => 10110 => 00100 => 1 = 2 - 1
01110 => 01110 => 00110 => 2 = 3 - 1
01111 => 11110 => 00111 => 3 = 4 - 1
10000 => 00001 => 10111 => 3 = 4 - 1
10001 => 10001 => 10110 => 2 = 3 - 1
10010 => 01001 => 10100 => 1 = 2 - 1
10011 => 11001 => 10101 => 1 = 2 - 1
1111000010 => 0100001111 => 1111011100 => ? = 5 - 1
1111111101 => 1011111111 => ? => ? = 9 - 1
1110111101 => 1011110111 => 1110011100 => ? = 4 - 1
1110110111 => 1110110111 => 1110010011 => ? = 4 - 1
1101111011 => 1101111011 => 1100111001 => ? = 4 - 1
1101101011 => 1101011011 => 1100100001 => ? = 3 - 1
1101011011 => 1101101011 => 1100001001 => ? = 3 - 1
1101010111 => 1110101011 => 1100000011 => ? = 3 - 1
1011110111 => 1110111101 => 1001110011 => ? = 4 - 1
1000000010 => 0100000001 => 1011111100 => ? = 7 - 1
10010101010 => 01010101001 => 10100000000 => ? = 2 - 1
10100101010 => 01010100101 => 10001000000 => ? = 2 - 1
=> => => ? = 1 - 1
0111111111 => 1111111110 => 0011111111 => ? = 9 - 1
11010101000 => 00010101011 => 11000000011 => ? = 3 - 1
11010100100 => 00100101011 => 11000001001 => ? = 3 - 1
11010010100 => 00101001011 => 11000100001 => ? = 3 - 1
11001010100 => 00101010011 => 11010000001 => ? = 3 - 1
10101010100 => 00101010101 => 10000000001 => ? = 2 - 1
00101010011 => 11001010100 => 01000000101 => ? = 2 - 1
00100101011 => 11010100100 => 01001000001 => ? = 2 - 1
0000000010 => 0100000000 => 0111111100 => ? = 8 - 1
0000111110 => 0111110000 => 0111011110 => ? = 5 - 1
0011111110 => 0111111100 => ? => ? = 7 - 1
10010010101 => 10101001001 => 10100100000 => ? = 2 - 1
01001010101 => 10101010010 => 00010000000 => ? = 2 - 1
01010100101 => 10100101010 => 00000001000 => ? = 2 - 1
01010101010 => 01010101010 => 00000000000 => ? = 1 - 1
0111111100 => ? => ? => ? = 7 - 1
01101010100 => 00101010110 => ? => ? = 2 - 1
01101001010 => ? => ? => ? = 2 - 1
01010110100 => 00101101010 => ? => ? = 2 - 1
11110001000 => 00010001111 => ? => ? = 5 - 1
11000111000 => 00011100011 => ? => ? = 3 - 1
11000100011 => 11000100011 => ? => ? = 3 - 1
00011100011 => 11000111000 => ? => ? = 3 - 1
00010001111 => 11110001000 => ? => ? = 4 - 1
Description
The length of the longest run of ones in a binary word.
Matching statistic: St000381
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
St000381: Integer compositions ⟶ ℤResult quality: 71% ●values known / values provided: 71%●distinct values known / distinct values provided: 100%
Values
0 => [2] => 10 => [1,1] => 1
1 => [1,1] => 11 => [2] => 2
00 => [3] => 100 => [1,2] => 2
01 => [2,1] => 101 => [1,1,1] => 1
10 => [1,2] => 110 => [2,1] => 2
11 => [1,1,1] => 111 => [3] => 3
000 => [4] => 1000 => [1,3] => 3
001 => [3,1] => 1001 => [1,2,1] => 2
010 => [2,2] => 1010 => [1,1,1,1] => 1
011 => [2,1,1] => 1011 => [1,1,2] => 2
100 => [1,3] => 1100 => [2,2] => 2
101 => [1,2,1] => 1101 => [2,1,1] => 2
110 => [1,1,2] => 1110 => [3,1] => 3
111 => [1,1,1,1] => 1111 => [4] => 4
0000 => [5] => 10000 => [1,4] => 4
0001 => [4,1] => 10001 => [1,3,1] => 3
0010 => [3,2] => 10010 => [1,2,1,1] => 2
0011 => [3,1,1] => 10011 => [1,2,2] => 2
0100 => [2,3] => 10100 => [1,1,1,2] => 2
0101 => [2,2,1] => 10101 => [1,1,1,1,1] => 1
0110 => [2,1,2] => 10110 => [1,1,2,1] => 2
0111 => [2,1,1,1] => 10111 => [1,1,3] => 3
1000 => [1,4] => 11000 => [2,3] => 3
1001 => [1,3,1] => 11001 => [2,2,1] => 2
1010 => [1,2,2] => 11010 => [2,1,1,1] => 2
1011 => [1,2,1,1] => 11011 => [2,1,2] => 2
1100 => [1,1,3] => 11100 => [3,2] => 3
1101 => [1,1,2,1] => 11101 => [3,1,1] => 3
1110 => [1,1,1,2] => 11110 => [4,1] => 4
1111 => [1,1,1,1,1] => 11111 => [5] => 5
00000 => [6] => 100000 => [1,5] => 5
00001 => [5,1] => 100001 => [1,4,1] => 4
00010 => [4,2] => 100010 => [1,3,1,1] => 3
00011 => [4,1,1] => 100011 => [1,3,2] => 3
00100 => [3,3] => 100100 => [1,2,1,2] => 2
00101 => [3,2,1] => 100101 => [1,2,1,1,1] => 2
00110 => [3,1,2] => 100110 => [1,2,2,1] => 2
00111 => [3,1,1,1] => 100111 => [1,2,3] => 3
01000 => [2,4] => 101000 => [1,1,1,3] => 3
01001 => [2,3,1] => 101001 => [1,1,1,2,1] => 2
01010 => [2,2,2] => 101010 => [1,1,1,1,1,1] => 1
01011 => [2,2,1,1] => 101011 => [1,1,1,1,2] => 2
01100 => [2,1,3] => 101100 => [1,1,2,2] => 2
01101 => [2,1,2,1] => 101101 => [1,1,2,1,1] => 2
01110 => [2,1,1,2] => 101110 => [1,1,3,1] => 3
01111 => [2,1,1,1,1] => 101111 => [1,1,4] => 4
10000 => [1,5] => 110000 => [2,4] => 4
10001 => [1,4,1] => 110001 => [2,3,1] => 3
10010 => [1,3,2] => 110010 => [2,2,1,1] => 2
10011 => [1,3,1,1] => 110011 => [2,2,2] => 2
000001111 => [6,1,1,1,1] => 1000001111 => [1,5,4] => ? = 5
000010111 => [5,2,1,1,1] => 1000010111 => [1,4,1,1,3] => ? = 4
000011011 => [5,1,2,1,1] => 1000011011 => [1,4,2,1,2] => ? = 4
000011101 => [5,1,1,2,1] => 1000011101 => [1,4,3,1,1] => ? = 4
000100111 => [4,3,1,1,1] => 1000100111 => [1,3,1,2,3] => ? = 3
000101011 => [4,2,2,1,1] => 1000101011 => [1,3,1,1,1,1,2] => ? = 3
000101101 => [4,2,1,2,1] => 1000101101 => [1,3,1,1,2,1,1] => ? = 3
000110011 => [4,1,3,1,1] => 1000110011 => [1,3,2,2,2] => ? = 3
000110101 => [4,1,2,2,1] => 1000110101 => [1,3,2,1,1,1,1] => ? = 3
000110110 => [4,1,2,1,2] => 1000110110 => [1,3,2,1,2,1] => ? = 3
000111001 => [4,1,1,3,1] => 1000111001 => [1,3,3,2,1] => ? = 3
000111010 => [4,1,1,2,2] => 1000111010 => [1,3,3,1,1,1] => ? = 3
001000000 => [3,7] => 1001000000 => [1,2,1,6] => ? = 6
001000111 => [3,4,1,1,1] => 1001000111 => [1,2,1,3,3] => ? = 3
001001011 => [3,3,2,1,1] => 1001001011 => [1,2,1,2,1,1,2] => ? = 2
001001101 => [3,3,1,2,1] => 1001001101 => [1,2,1,2,2,1,1] => ? = 2
001001110 => [3,3,1,1,2] => 1001001110 => [1,2,1,2,3,1] => ? = 3
001010011 => [3,2,3,1,1] => 1001010011 => [1,2,1,1,1,2,2] => ? = 2
001010101 => [3,2,2,2,1] => 1001010101 => [1,2,1,1,1,1,1,1,1] => ? = 2
001010110 => [3,2,2,1,2] => 1001010110 => [1,2,1,1,1,1,2,1] => ? = 2
001011001 => [3,2,1,3,1] => 1001011001 => [1,2,1,1,2,2,1] => ? = 2
001011010 => [3,2,1,2,2] => 1001011010 => [1,2,1,1,2,1,1,1] => ? = 2
001100011 => [3,1,4,1,1] => 1001100011 => [1,2,2,3,2] => ? = 3
001100101 => [3,1,3,2,1] => 1001100101 => [1,2,2,2,1,1,1] => ? = 2
001100110 => [3,1,3,1,2] => 1001100110 => [1,2,2,2,2,1] => ? = 2
001101001 => [3,1,2,3,1] => 1001101001 => [1,2,2,1,1,2,1] => ? = 2
001101010 => [3,1,2,2,2] => 1001101010 => [1,2,2,1,1,1,1,1] => ? = 2
010000000 => [2,8] => 1010000000 => [1,1,1,7] => ? = 7
010000010 => [2,6,2] => 1010000010 => [1,1,1,5,1,1] => ? = 5
010000111 => [2,5,1,1,1] => 1010000111 => [1,1,1,4,3] => ? = 4
010001011 => [2,4,2,1,1] => 1010001011 => [1,1,1,3,1,1,2] => ? = 3
010001101 => [2,4,1,2,1] => 1010001101 => [1,1,1,3,2,1,1] => ? = 3
010001110 => [2,4,1,1,2] => 1010001110 => [1,1,1,3,3,1] => ? = 3
010010011 => [2,3,3,1,1] => 1010010011 => [1,1,1,2,1,2,2] => ? = 2
010010101 => [2,3,2,2,1] => 1010010101 => [1,1,1,2,1,1,1,1,1] => ? = 2
010010110 => [2,3,2,1,2] => 1010010110 => [1,1,1,2,1,1,2,1] => ? = 2
010011010 => [2,3,1,2,2] => 1010011010 => [1,1,1,2,2,1,1,1] => ? = 2
010100000 => [2,2,6] => 1010100000 => [1,1,1,1,1,5] => ? = 5
010100011 => [2,2,4,1,1] => 1010100011 => [1,1,1,1,1,3,2] => ? = 3
010100101 => [2,2,3,2,1] => 1010100101 => [1,1,1,1,1,2,1,1,1] => ? = 2
010100110 => [2,2,3,1,2] => 1010100110 => [1,1,1,1,1,2,2,1] => ? = 2
010101001 => [2,2,2,3,1] => 1010101001 => [1,1,1,1,1,1,1,2,1] => ? = 2
011000000 => [2,1,7] => 1011000000 => [1,1,2,6] => ? = 6
011000011 => [2,1,5,1,1] => 1011000011 => [1,1,2,4,2] => ? = 4
011000101 => [2,1,4,2,1] => 1011000101 => [1,1,2,3,1,1,1] => ? = 3
011010000 => [2,1,2,5] => 1011010000 => [1,1,2,1,1,4] => ? = 4
011100000 => [2,1,1,6] => 1011100000 => [1,1,3,5] => ? = 5
011110100 => [2,1,1,1,2,3] => 1011110100 => [1,1,4,1,1,2] => ? = 4
011111000 => [2,1,1,1,1,4] => 1011111000 => [1,1,5,3] => ? = 5
011111010 => [2,1,1,1,1,2,2] => 1011111010 => [1,1,5,1,1,1] => ? = 5
Description
The largest part of an integer composition.
Matching statistic: St000983
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
St000983: Binary words ⟶ ℤResult quality: 62% ●values known / values provided: 62%●distinct values known / distinct values provided: 90%
Values
0 => [2] => 10 => 11 => 1
1 => [1,1] => 11 => 10 => 2
00 => [3] => 100 => 110 => 2
01 => [2,1] => 101 => 111 => 1
10 => [1,2] => 110 => 100 => 2
11 => [1,1,1] => 111 => 101 => 3
000 => [4] => 1000 => 1101 => 3
001 => [3,1] => 1001 => 1100 => 2
010 => [2,2] => 1010 => 1111 => 1
011 => [2,1,1] => 1011 => 1110 => 2
100 => [1,3] => 1100 => 1001 => 2
101 => [1,2,1] => 1101 => 1000 => 2
110 => [1,1,2] => 1110 => 1011 => 3
111 => [1,1,1,1] => 1111 => 1010 => 4
0000 => [5] => 10000 => 11010 => 4
0001 => [4,1] => 10001 => 11011 => 3
0010 => [3,2] => 10010 => 11000 => 2
0011 => [3,1,1] => 10011 => 11001 => 2
0100 => [2,3] => 10100 => 11110 => 2
0101 => [2,2,1] => 10101 => 11111 => 1
0110 => [2,1,2] => 10110 => 11100 => 2
0111 => [2,1,1,1] => 10111 => 11101 => 3
1000 => [1,4] => 11000 => 10010 => 3
1001 => [1,3,1] => 11001 => 10011 => 2
1010 => [1,2,2] => 11010 => 10000 => 2
1011 => [1,2,1,1] => 11011 => 10001 => 2
1100 => [1,1,3] => 11100 => 10110 => 3
1101 => [1,1,2,1] => 11101 => 10111 => 3
1110 => [1,1,1,2] => 11110 => 10100 => 4
1111 => [1,1,1,1,1] => 11111 => 10101 => 5
00000 => [6] => 100000 => 110101 => 5
00001 => [5,1] => 100001 => 110100 => 4
00010 => [4,2] => 100010 => 110111 => 3
00011 => [4,1,1] => 100011 => 110110 => 3
00100 => [3,3] => 100100 => 110001 => 2
00101 => [3,2,1] => 100101 => 110000 => 2
00110 => [3,1,2] => 100110 => 110011 => 2
00111 => [3,1,1,1] => 100111 => 110010 => 3
01000 => [2,4] => 101000 => 111101 => 3
01001 => [2,3,1] => 101001 => 111100 => 2
01010 => [2,2,2] => 101010 => 111111 => 1
01011 => [2,2,1,1] => 101011 => 111110 => 2
01100 => [2,1,3] => 101100 => 111001 => 2
01101 => [2,1,2,1] => 101101 => 111000 => 2
01110 => [2,1,1,2] => 101110 => 111011 => 3
01111 => [2,1,1,1,1] => 101111 => 111010 => 4
10000 => [1,5] => 110000 => 100101 => 4
10001 => [1,4,1] => 110001 => 100100 => 3
10010 => [1,3,2] => 110010 => 100111 => 2
10011 => [1,3,1,1] => 110011 => 100110 => 2
000000000 => [10] => 1000000000 => 1101010101 => ? = 9
000000010 => [8,2] => 1000000010 => 1101010111 => ? = 7
000000100 => [7,3] => 1000000100 => 1101010001 => ? = 6
000000110 => [7,1,2] => 1000000110 => 1101010011 => ? = 6
000001010 => [6,2,2] => 1000001010 => 1101011111 => ? = 5
000001110 => [6,1,1,2] => 1000001110 => 1101011011 => ? = 5
000001111 => [6,1,1,1,1] => 1000001111 => 1101011010 => ? = 5
000010110 => [5,2,1,2] => 1000010110 => 1101000011 => ? = 4
000010111 => [5,2,1,1,1] => 1000010111 => 1101000010 => ? = 4
000011011 => [5,1,2,1,1] => 1000011011 => 1101001110 => ? = 4
000011101 => [5,1,1,2,1] => 1000011101 => 1101001000 => ? = 4
000011110 => [5,1,1,1,2] => 1000011110 => 1101001011 => ? = 4
000100111 => [4,3,1,1,1] => 1000100111 => 1101110010 => ? = 3
000101011 => [4,2,2,1,1] => 1000101011 => 1101111110 => ? = 3
000101101 => [4,2,1,2,1] => 1000101101 => 1101111000 => ? = 3
000101110 => [4,2,1,1,2] => 1000101110 => 1101111011 => ? = 3
000110011 => [4,1,3,1,1] => 1000110011 => 1101100110 => ? = 3
000110101 => [4,1,2,2,1] => 1000110101 => 1101100000 => ? = 3
000110110 => [4,1,2,1,2] => 1000110110 => 1101100011 => ? = 3
000111001 => [4,1,1,3,1] => 1000111001 => 1101101100 => ? = 3
000111010 => [4,1,1,2,2] => 1000111010 => 1101101111 => ? = 3
000111110 => [4,1,1,1,1,2] => 1000111110 => 1101101011 => ? = 5
001000000 => [3,7] => 1001000000 => 1100010101 => ? = 6
001000111 => [3,4,1,1,1] => 1001000111 => 1100010010 => ? = 3
001001011 => [3,3,2,1,1] => 1001001011 => 1100011110 => ? = 2
001001101 => [3,3,1,2,1] => 1001001101 => 1100011000 => ? = 2
001001110 => [3,3,1,1,2] => 1001001110 => 1100011011 => ? = 3
001010011 => [3,2,3,1,1] => 1001010011 => 1100000110 => ? = 2
001010101 => [3,2,2,2,1] => 1001010101 => 1100000000 => ? = 2
001010110 => [3,2,2,1,2] => 1001010110 => 1100000011 => ? = 2
001011001 => [3,2,1,3,1] => 1001011001 => 1100001100 => ? = 2
001011010 => [3,2,1,2,2] => 1001011010 => 1100001111 => ? = 2
001011110 => [3,2,1,1,1,2] => 1001011110 => 1100001011 => ? = 4
001100011 => [3,1,4,1,1] => 1001100011 => 1100110110 => ? = 3
001100101 => [3,1,3,2,1] => 1001100101 => 1100110000 => ? = 2
001100110 => [3,1,3,1,2] => 1001100110 => 1100110011 => ? = 2
001101001 => [3,1,2,3,1] => 1001101001 => 1100111100 => ? = 2
001101010 => [3,1,2,2,2] => 1001101010 => 1100111111 => ? = 2
001111110 => [3,1,1,1,1,1,2] => 1001111110 => 1100101011 => ? = 6
010000000 => [2,8] => 1010000000 => 1111010101 => ? = 7
010000010 => [2,6,2] => 1010000010 => 1111010111 => ? = 5
010000111 => [2,5,1,1,1] => 1010000111 => 1111010010 => ? = 4
010001011 => [2,4,2,1,1] => 1010001011 => 1111011110 => ? = 3
010001101 => [2,4,1,2,1] => 1010001101 => 1111011000 => ? = 3
010001110 => [2,4,1,1,2] => 1010001110 => 1111011011 => ? = 3
010010011 => [2,3,3,1,1] => 1010010011 => 1111000110 => ? = 2
010010101 => [2,3,2,2,1] => 1010010101 => 1111000000 => ? = 2
010010110 => [2,3,2,1,2] => 1010010110 => 1111000011 => ? = 2
010011010 => [2,3,1,2,2] => 1010011010 => 1111001111 => ? = 2
010100000 => [2,2,6] => 1010100000 => 1111110101 => ? = 5
Description
The length of the longest alternating subword. This is the length of the longest consecutive subword of the form $010...$ or of the form $101...$.
Matching statistic: St000774
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000774: Graphs ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 70%
Values
0 => [2] => [1,1] => ([(0,1)],2)
 => 1
1 => [1,1] => [2] => ([],2)
 => 2
00 => [3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
01 => [2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
10 => [1,2] => [1,2] => ([(1,2)],3)
 => 2
11 => [1,1,1] => [3] => ([],3)
 => 3
000 => [4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
001 => [3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
010 => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
011 => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
100 => [1,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 2
101 => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => 2
110 => [1,1,2] => [1,3] => ([(2,3)],4)
 => 3
111 => [1,1,1,1] => [4] => ([],4)
 => 4
0000 => [5] => [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)
 => 4
0001 => [4,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
0010 => [3,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
0011 => [3,1,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
0100 => [2,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
0101 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
0110 => [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
0111 => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
1000 => [1,4] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
1001 => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
1010 => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 2
1011 => [1,2,1,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 2
1100 => [1,1,3] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => 3
1101 => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
 => 3
1110 => [1,1,1,2] => [1,4] => ([(3,4)],5)
 => 4
1111 => [1,1,1,1,1] => [5] => ([],5)
 => 5
00000 => [6] => [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)
 => 5
00001 => [5,1] => [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)
 => 4
00010 => [4,2] => [1,2,1,1,1] => ([(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
00011 => [4,1,1] => [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)
 => 3
00100 => [3,3] => [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)
 => 2
00101 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
00110 => [3,1,2] => [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)
 => 2
00111 => [3,1,1,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
01000 => [2,4] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
01001 => [2,3,1] => [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)
 => 2
01010 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
01011 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
01100 => [2,1,3] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
01101 => [2,1,2,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
01110 => [2,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
01111 => [2,1,1,1,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
10000 => [1,5] => [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)
 => 4
10001 => [1,4,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
10010 => [1,3,2] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
10011 => [1,3,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
001100 => [3,1,3] => [1,1,3,1,1] => ([(0,5),(0,6),(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)
 => ? = 2
0000000 => [8] => [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)
 => ? = 7
0000001 => [7,1] => [2,1,1,1,1,1,1] => ([(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)
 => ? = 6
0000010 => [6,2] => [1,2,1,1,1,1,1] => ([(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)
 => ? = 5
0000011 => [6,1,1] => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(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)
 => ? = 5
0000100 => [5,3] => [1,1,2,1,1,1,1] => ([(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)
 => ? = 4
0000101 => [5,2,1] => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(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)
 => ? = 4
0000110 => [5,1,2] => [1,3,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(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)
 => ? = 4
0000111 => [5,1,1,1] => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(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)
 => ? = 4
0001000 => [4,4] => [1,1,1,2,1,1,1] => ([(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)
 => ? = 3
0001001 => [4,3,1] => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(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)
 => ? = 3
0001010 => [4,2,2] => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(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)
 => ? = 3
0001011 => [4,2,1,1] => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(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)
 => ? = 3
0001100 => [4,1,3] => [1,1,3,1,1,1] => ([(0,5),(0,6),(0,7),(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)
 => ? = 3
0001101 => [4,1,2,1] => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 3
0001110 => [4,1,1,2] => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 3
0001111 => [4,1,1,1,1] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
0010000 => [3,5] => [1,1,1,1,2,1,1] => ([(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)
 => ? = 4
0010001 => [3,4,1] => [2,1,1,2,1,1] => ([(0,6),(0,7),(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)
 => ? = 3
0010010 => [3,3,2] => [1,2,1,2,1,1] => ([(0,6),(0,7),(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)
 => ? = 2
0010011 => [3,3,1,1] => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(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)
 => ? = 2
0010100 => [3,2,3] => [1,1,2,2,1,1] => ([(0,6),(0,7),(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)
 => ? = 2
0010101 => [3,2,2,1] => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 2
0010110 => [3,2,1,2] => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 2
0010111 => [3,2,1,1,1] => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
0011000 => [3,1,4] => [1,1,1,3,1,1] => ([(0,6),(0,7),(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)
 => ? = 3
0011001 => [3,1,3,1] => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(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)
 => ? = 2
0011010 => [3,1,2,2] => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(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)
 => ? = 2
0011011 => [3,1,2,1,1] => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
0011100 => [3,1,1,3] => [1,1,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(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)
 => ? = 3
0011101 => [3,1,1,2,1] => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
0011110 => [3,1,1,1,2] => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
0011111 => [3,1,1,1,1,1] => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 5
0100000 => [2,6] => [1,1,1,1,1,2,1] => ([(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)
 => ? = 5
0100001 => [2,5,1] => [2,1,1,1,2,1] => ([(0,7),(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)
 => ? = 4
0100010 => [2,4,2] => [1,2,1,1,2,1] => ([(0,7),(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)
 => ? = 3
0100011 => [2,4,1,1] => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(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)
 => ? = 3
0100100 => [2,3,3] => [1,1,2,1,2,1] => ([(0,7),(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)
 => ? = 2
0100101 => [2,3,2,1] => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 2
0100110 => [2,3,1,2] => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 2
0100111 => [2,3,1,1,1] => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
0101000 => [2,2,4] => [1,1,1,2,2,1] => ([(0,7),(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)
 => ? = 3
0101001 => [2,2,3,1] => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(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)
 => ? = 2
0101010 => [2,2,2,2] => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(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)
 => ? = 1
0101011 => [2,2,2,1,1] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
0101100 => [2,2,1,3] => [1,1,3,2,1] => ([(0,7),(1,6),(1,7),(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)
 => ? = 2
0101101 => [2,2,1,2,1] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
0101110 => [2,2,1,1,2] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
0101111 => [2,2,1,1,1,1] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
0110000 => [2,1,5] => [1,1,1,1,3,1] => ([(0,7),(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)
 => ? = 4
Description
The maximal multiplicity of a Laplacian eigenvalue in a graph.
Matching statistic: St000771
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 60%
Values
0 => [2] => [1,1] => ([(0,1)],2)
 => 1
1 => [1,1] => [2] => ([],2)
 => ? = 2
00 => [3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
01 => [2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
10 => [1,2] => [1,2] => ([(1,2)],3)
 => ? = 2
11 => [1,1,1] => [3] => ([],3)
 => ? = 3
000 => [4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
001 => [3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
010 => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
011 => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
100 => [1,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
101 => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 2
110 => [1,1,2] => [1,3] => ([(2,3)],4)
 => ? = 3
111 => [1,1,1,1] => [4] => ([],4)
 => ? = 4
0000 => [5] => [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)
 => 4
0001 => [4,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
0010 => [3,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
0011 => [3,1,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
0100 => [2,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
0101 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
0110 => [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
0111 => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
1000 => [1,4] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3
1001 => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2
1010 => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2
1011 => [1,2,1,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 2
1100 => [1,1,3] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 3
1101 => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 3
1110 => [1,1,1,2] => [1,4] => ([(3,4)],5)
 => ? = 4
1111 => [1,1,1,1,1] => [5] => ([],5)
 => ? = 5
00000 => [6] => [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)
 => 5
00001 => [5,1] => [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)
 => 4
00010 => [4,2] => [1,2,1,1,1] => ([(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
00011 => [4,1,1] => [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)
 => 3
00100 => [3,3] => [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)
 => 2
00101 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
00110 => [3,1,2] => [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)
 => 2
00111 => [3,1,1,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
01000 => [2,4] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
01001 => [2,3,1] => [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)
 => 2
01010 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
01011 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
01100 => [2,1,3] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
01101 => [2,1,2,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
01110 => [2,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
01111 => [2,1,1,1,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
10000 => [1,5] => [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)
 => ? = 4
10001 => [1,4,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3
10010 => [1,3,2] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
10011 => [1,3,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
10100 => [1,2,3] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
10101 => [1,2,2,1] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
10110 => [1,2,1,2] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
10111 => [1,2,1,1,1] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 3
11000 => [1,1,4] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3
11001 => [1,1,3,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3
11010 => [1,1,2,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3
11011 => [1,1,2,1,1] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 3
11100 => [1,1,1,3] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
 => ? = 4
11101 => [1,1,1,2,1] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 4
11110 => [1,1,1,1,2] => [1,5] => ([(4,5)],6)
 => ? = 5
11111 => [1,1,1,1,1,1] => [6] => ([],6)
 => ? = 6
000000 => [7] => [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)
 => 6
000001 => [6,1] => [2,1,1,1,1,1] => ([(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)
 => 5
000010 => [5,2] => [1,2,1,1,1,1] => ([(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)
 => 4
000011 => [5,1,1] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(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)
 => 4
000100 => [4,3] => [1,1,2,1,1,1] => ([(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)
 => 3
000101 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(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)
 => 3
000110 => [4,1,2] => [1,3,1,1,1] => ([(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)
 => 3
000111 => [4,1,1,1] => [4,1,1,1] => ([(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)
 => 3
001000 => [3,4] => [1,1,1,2,1,1] => ([(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)
 => 3
001001 => [3,3,1] => [2,1,2,1,1] => ([(0,5),(0,6),(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)
 => 2
001010 => [3,2,2] => [1,2,2,1,1] => ([(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)
 => 2
001011 => [3,2,1,1] => [3,2,1,1] => ([(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)
 => 2
001100 => [3,1,3] => [1,1,3,1,1] => ([(0,5),(0,6),(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)
 => 2
001101 => [3,1,2,1] => [2,3,1,1] => ([(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)
 => 2
001110 => [3,1,1,2] => [1,4,1,1] => ([(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)
 => 3
001111 => [3,1,1,1,1] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 4
010000 => [2,5] => [1,1,1,1,2,1] => ([(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)
 => 4
010001 => [2,4,1] => [2,1,1,2,1] => ([(0,6),(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)
 => 3
010010 => [2,3,2] => [1,2,1,2,1] => ([(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)
 => 2
100000 => [1,6] => [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)
 => ? = 5
100001 => [1,5,1] => [2,1,1,1,2] => ([(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)
 => ? = 4
100010 => [1,4,2] => [1,2,1,1,2] => ([(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)
 => ? = 3
100011 => [1,4,1,1] => [3,1,1,2] => ([(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)
 => ? = 3
100100 => [1,3,3] => [1,1,2,1,2] => ([(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)
 => ? = 2
100101 => [1,3,2,1] => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
100110 => [1,3,1,2] => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
100111 => [1,3,1,1,1] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
101000 => [1,2,4] => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
101001 => [1,2,3,1] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
101010 => [1,2,2,2] => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
101011 => [1,2,2,1,1] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
101100 => [1,2,1,3] => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
101101 => [1,2,1,2,1] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
101110 => [1,2,1,1,2] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
101111 => [1,2,1,1,1,1] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 4
110000 => [1,1,5] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 4
110001 => [1,1,4,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
110010 => [1,1,3,2] => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
Description
The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian $$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$ Its eigenvalues are $0,4,4,6$, so the statistic is $2$. The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore statistic $1$.
Matching statistic: St001235
Mapping
Mp00104: Binary words —reverse⟶ Binary words
Mp00269: Binary words —flag zeros to zeros⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
St001235: Integer compositions ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 60%
Values
0 => 0 => 0 => [2] => 1
1 => 1 => 1 => [1,1] => 2
00 => 00 => 01 => [2,1] => 2
01 => 10 => 00 => [3] => 1
10 => 01 => 10 => [1,2] => 2
11 => 11 => 11 => [1,1,1] => 3
000 => 000 => 011 => [2,1,1] => 3
001 => 100 => 010 => [2,2] => 2
010 => 010 => 000 => [4] => 1
011 => 110 => 001 => [3,1] => 2
100 => 001 => 101 => [1,2,1] => 2
101 => 101 => 100 => [1,3] => 2
110 => 011 => 110 => [1,1,2] => 3
111 => 111 => 111 => [1,1,1,1] => 4
0000 => 0000 => 0111 => [2,1,1,1] => 4
0001 => 1000 => 0110 => [2,1,2] => 3
0010 => 0100 => 0100 => [2,3] => 2
0011 => 1100 => 0101 => [2,2,1] => 2
0100 => 0010 => 0001 => [4,1] => 2
0101 => 1010 => 0000 => [5] => 1
0110 => 0110 => 0010 => [3,2] => 2
0111 => 1110 => 0011 => [3,1,1] => 3
1000 => 0001 => 1011 => [1,2,1,1] => 3
1001 => 1001 => 1010 => [1,2,2] => 2
1010 => 0101 => 1000 => [1,4] => 2
1011 => 1101 => 1001 => [1,3,1] => 2
1100 => 0011 => 1101 => [1,1,2,1] => 3
1101 => 1011 => 1100 => [1,1,3] => 3
1110 => 0111 => 1110 => [1,1,1,2] => 4
1111 => 1111 => 1111 => [1,1,1,1,1] => 5
00000 => 00000 => 01111 => [2,1,1,1,1] => 5
00001 => 10000 => 01110 => [2,1,1,2] => 4
00010 => 01000 => 01100 => [2,1,3] => 3
00011 => 11000 => 01101 => [2,1,2,1] => 3
00100 => 00100 => 01001 => [2,3,1] => 2
00101 => 10100 => 01000 => [2,4] => 2
00110 => 01100 => 01010 => [2,2,2] => 2
00111 => 11100 => 01011 => [2,2,1,1] => 3
01000 => 00010 => 00011 => [4,1,1] => 3
01001 => 10010 => 00010 => [4,2] => 2
01010 => 01010 => 00000 => [6] => 1
01011 => 11010 => 00001 => [5,1] => 2
01100 => 00110 => 00101 => [3,2,1] => 2
01101 => 10110 => 00100 => [3,3] => 2
01110 => 01110 => 00110 => [3,1,2] => 3
01111 => 11110 => 00111 => [3,1,1,1] => 4
10000 => 00001 => 10111 => [1,2,1,1,1] => 4
10001 => 10001 => 10110 => [1,2,1,2] => 3
10010 => 01001 => 10100 => [1,2,3] => 2
10011 => 11001 => 10101 => [1,2,2,1] => 2
000000 => 000000 => 011111 => [2,1,1,1,1,1] => ? = 6
000001 => 100000 => 011110 => [2,1,1,1,2] => ? = 5
000010 => 010000 => 011100 => [2,1,1,3] => ? = 4
000011 => 110000 => 011101 => [2,1,1,2,1] => ? = 4
000100 => 001000 => 011001 => [2,1,3,1] => ? = 3
000101 => 101000 => 011000 => [2,1,4] => ? = 3
000110 => 011000 => 011010 => [2,1,2,2] => ? = 3
000111 => 111000 => 011011 => [2,1,2,1,1] => ? = 3
001000 => 000100 => 010011 => [2,3,1,1] => ? = 3
001001 => 100100 => 010010 => [2,3,2] => ? = 2
001010 => 010100 => 010000 => [2,5] => ? = 2
001011 => 110100 => 010001 => [2,4,1] => ? = 2
001100 => 001100 => 010101 => [2,2,2,1] => ? = 2
001101 => 101100 => 010100 => [2,2,3] => ? = 2
001110 => 011100 => 010110 => [2,2,1,2] => ? = 3
001111 => 111100 => 010111 => [2,2,1,1,1] => ? = 4
010000 => 000010 => 000111 => [4,1,1,1] => ? = 4
010001 => 100010 => 000110 => [4,1,2] => ? = 3
010010 => 010010 => 000100 => [4,3] => ? = 2
010011 => 110010 => 000101 => [4,2,1] => ? = 2
010100 => 001010 => 000001 => [6,1] => ? = 2
010101 => 101010 => 000000 => [7] => ? = 1
010110 => 011010 => 000010 => [5,2] => ? = 2
010111 => 111010 => 000011 => [5,1,1] => ? = 3
011000 => 000110 => 001011 => [3,2,1,1] => ? = 3
011001 => 100110 => 001010 => [3,2,2] => ? = 2
011010 => 010110 => 001000 => [3,4] => ? = 2
011011 => 110110 => 001001 => [3,3,1] => ? = 2
011100 => 001110 => 001101 => [3,1,2,1] => ? = 3
011101 => 101110 => 001100 => [3,1,3] => ? = 3
011110 => 011110 => 001110 => [3,1,1,2] => ? = 4
011111 => 111110 => 001111 => [3,1,1,1,1] => ? = 5
100000 => 000001 => 101111 => [1,2,1,1,1,1] => ? = 5
100001 => 100001 => 101110 => [1,2,1,1,2] => ? = 4
100010 => 010001 => 101100 => [1,2,1,3] => ? = 3
100011 => 110001 => 101101 => [1,2,1,2,1] => ? = 3
100100 => 001001 => 101001 => [1,2,3,1] => ? = 2
100101 => 101001 => 101000 => [1,2,4] => ? = 2
100110 => 011001 => 101010 => [1,2,2,2] => ? = 2
100111 => 111001 => 101011 => [1,2,2,1,1] => ? = 3
101000 => 000101 => 100011 => [1,4,1,1] => ? = 3
101001 => 100101 => 100010 => [1,4,2] => ? = 2
101010 => 010101 => 100000 => [1,6] => ? = 2
101011 => 110101 => 100001 => [1,5,1] => ? = 2
101100 => 001101 => 100101 => [1,3,2,1] => ? = 2
101101 => 101101 => 100100 => [1,3,3] => ? = 2
101110 => 011101 => 100110 => [1,3,1,2] => ? = 3
101111 => 111101 => 100111 => [1,3,1,1,1] => ? = 4
110000 => 000011 => 110111 => [1,1,2,1,1,1] => ? = 4
110001 => 100011 => 110110 => [1,1,2,1,2] => ? = 3
Description
The global dimension of the corresponding Comp-Nakayama algebra. We identify the composition [n1-1,n2-1,...,nr-1] with the Nakayama algebra with Kupisch series [n1,n1-1,...,2,n2,n2-1,...,2,...,nr,nr-1,...,3,2,1]. We call such Nakayama algebras with Kupisch series corresponding to a integer composition "Comp-Nakayama algebra".