Processing math: 100%

Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St000983
(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
St000983: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [2] => 10 => 01 => 2
1 => [1,1] => 11 => 00 => 1
00 => [3] => 100 => 011 => 2
01 => [2,1] => 101 => 010 => 3
10 => [1,2] => 110 => 001 => 2
11 => [1,1,1] => 111 => 000 => 1
000 => [4] => 1000 => 0111 => 2
001 => [3,1] => 1001 => 0110 => 2
010 => [2,2] => 1010 => 0101 => 4
011 => [2,1,1] => 1011 => 0100 => 3
100 => [1,3] => 1100 => 0011 => 2
101 => [1,2,1] => 1101 => 0010 => 3
110 => [1,1,2] => 1110 => 0001 => 2
111 => [1,1,1,1] => 1111 => 0000 => 1
0000 => [5] => 10000 => 01111 => 2
0001 => [4,1] => 10001 => 01110 => 2
0010 => [3,2] => 10010 => 01101 => 3
0011 => [3,1,1] => 10011 => 01100 => 2
0100 => [2,3] => 10100 => 01011 => 4
0101 => [2,2,1] => 10101 => 01010 => 5
0110 => [2,1,2] => 10110 => 01001 => 3
0111 => [2,1,1,1] => 10111 => 01000 => 3
1000 => [1,4] => 11000 => 00111 => 2
1001 => [1,3,1] => 11001 => 00110 => 2
1010 => [1,2,2] => 11010 => 00101 => 4
1011 => [1,2,1,1] => 11011 => 00100 => 3
1100 => [1,1,3] => 11100 => 00011 => 2
1101 => [1,1,2,1] => 11101 => 00010 => 3
1110 => [1,1,1,2] => 11110 => 00001 => 2
1111 => [1,1,1,1,1] => 11111 => 00000 => 1
00000 => [6] => 100000 => 011111 => 2
00001 => [5,1] => 100001 => 011110 => 2
00010 => [4,2] => 100010 => 011101 => 3
00011 => [4,1,1] => 100011 => 011100 => 2
00100 => [3,3] => 100100 => 011011 => 3
00101 => [3,2,1] => 100101 => 011010 => 4
00110 => [3,1,2] => 100110 => 011001 => 2
00111 => [3,1,1,1] => 100111 => 011000 => 2
01000 => [2,4] => 101000 => 010111 => 4
01001 => [2,3,1] => 101001 => 010110 => 4
01010 => [2,2,2] => 101010 => 010101 => 6
01011 => [2,2,1,1] => 101011 => 010100 => 5
01100 => [2,1,3] => 101100 => 010011 => 3
01101 => [2,1,2,1] => 101101 => 010010 => 3
01110 => [2,1,1,2] => 101110 => 010001 => 3
01111 => [2,1,1,1,1] => 101111 => 010000 => 3
10000 => [1,5] => 110000 => 001111 => 2
10001 => [1,4,1] => 110001 => 001110 => 2
10010 => [1,3,2] => 110010 => 001101 => 3
10011 => [1,3,1,1] => 110011 => 001100 => 2
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: St000392
Mapping
Mp00104: Binary words —reverse⟶ Binary words
Mp00269: Binary words —flag zeros to zeros⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
St000392: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 => 0 => 1 => 1 = 2 - 1
1 => 1 => 1 => 0 => 0 = 1 - 1
00 => 00 => 01 => 10 => 1 = 2 - 1
01 => 10 => 00 => 11 => 2 = 3 - 1
10 => 01 => 10 => 01 => 1 = 2 - 1
11 => 11 => 11 => 00 => 0 = 1 - 1
000 => 000 => 011 => 100 => 1 = 2 - 1
001 => 100 => 010 => 101 => 1 = 2 - 1
010 => 010 => 000 => 111 => 3 = 4 - 1
011 => 110 => 001 => 110 => 2 = 3 - 1
100 => 001 => 101 => 010 => 1 = 2 - 1
101 => 101 => 100 => 011 => 2 = 3 - 1
110 => 011 => 110 => 001 => 1 = 2 - 1
111 => 111 => 111 => 000 => 0 = 1 - 1
0000 => 0000 => 0111 => 1000 => 1 = 2 - 1
0001 => 1000 => 0110 => 1001 => 1 = 2 - 1
0010 => 0100 => 0100 => 1011 => 2 = 3 - 1
0011 => 1100 => 0101 => 1010 => 1 = 2 - 1
0100 => 0010 => 0001 => 1110 => 3 = 4 - 1
0101 => 1010 => 0000 => 1111 => 4 = 5 - 1
0110 => 0110 => 0010 => 1101 => 2 = 3 - 1
0111 => 1110 => 0011 => 1100 => 2 = 3 - 1
1000 => 0001 => 1011 => 0100 => 1 = 2 - 1
1001 => 1001 => 1010 => 0101 => 1 = 2 - 1
1010 => 0101 => 1000 => 0111 => 3 = 4 - 1
1011 => 1101 => 1001 => 0110 => 2 = 3 - 1
1100 => 0011 => 1101 => 0010 => 1 = 2 - 1
1101 => 1011 => 1100 => 0011 => 2 = 3 - 1
1110 => 0111 => 1110 => 0001 => 1 = 2 - 1
1111 => 1111 => 1111 => 0000 => 0 = 1 - 1
00000 => 00000 => 01111 => 10000 => 1 = 2 - 1
00001 => 10000 => 01110 => 10001 => 1 = 2 - 1
00010 => 01000 => 01100 => 10011 => 2 = 3 - 1
00011 => 11000 => 01101 => 10010 => 1 = 2 - 1
00100 => 00100 => 01001 => 10110 => 2 = 3 - 1
00101 => 10100 => 01000 => 10111 => 3 = 4 - 1
00110 => 01100 => 01010 => 10101 => 1 = 2 - 1
00111 => 11100 => 01011 => 10100 => 1 = 2 - 1
01000 => 00010 => 00011 => 11100 => 3 = 4 - 1
01001 => 10010 => 00010 => 11101 => 3 = 4 - 1
01010 => 01010 => 00000 => 11111 => 5 = 6 - 1
01011 => 11010 => 00001 => 11110 => 4 = 5 - 1
01100 => 00110 => 00101 => 11010 => 2 = 3 - 1
01101 => 10110 => 00100 => 11011 => 2 = 3 - 1
01110 => 01110 => 00110 => 11001 => 2 = 3 - 1
01111 => 11110 => 00111 => 11000 => 2 = 3 - 1
10000 => 00001 => 10111 => 01000 => 1 = 2 - 1
10001 => 10001 => 10110 => 01001 => 1 = 2 - 1
10010 => 01001 => 10100 => 01011 => 2 = 3 - 1
10011 => 11001 => 10101 => 01010 => 1 = 2 - 1
=> => => => ? = 1 - 1
Description
The length of the longest run of ones in a binary word.
Matching statistic: St000982
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
St000982: Binary words ⟶ ℤResult quality: 80% ●values known / values provided: 80%●distinct values known / distinct values provided: 100%
Values
0 => [2] => 10 => 11 => 2
1 => [1,1] => 11 => 10 => 1
00 => [3] => 100 => 110 => 2
01 => [2,1] => 101 => 111 => 3
10 => [1,2] => 110 => 100 => 2
11 => [1,1,1] => 111 => 101 => 1
000 => [4] => 1000 => 1101 => 2
001 => [3,1] => 1001 => 1100 => 2
010 => [2,2] => 1010 => 1111 => 4
011 => [2,1,1] => 1011 => 1110 => 3
100 => [1,3] => 1100 => 1001 => 2
101 => [1,2,1] => 1101 => 1000 => 3
110 => [1,1,2] => 1110 => 1011 => 2
111 => [1,1,1,1] => 1111 => 1010 => 1
0000 => [5] => 10000 => 11010 => 2
0001 => [4,1] => 10001 => 11011 => 2
0010 => [3,2] => 10010 => 11000 => 3
0011 => [3,1,1] => 10011 => 11001 => 2
0100 => [2,3] => 10100 => 11110 => 4
0101 => [2,2,1] => 10101 => 11111 => 5
0110 => [2,1,2] => 10110 => 11100 => 3
0111 => [2,1,1,1] => 10111 => 11101 => 3
1000 => [1,4] => 11000 => 10010 => 2
1001 => [1,3,1] => 11001 => 10011 => 2
1010 => [1,2,2] => 11010 => 10000 => 4
1011 => [1,2,1,1] => 11011 => 10001 => 3
1100 => [1,1,3] => 11100 => 10110 => 2
1101 => [1,1,2,1] => 11101 => 10111 => 3
1110 => [1,1,1,2] => 11110 => 10100 => 2
1111 => [1,1,1,1,1] => 11111 => 10101 => 1
00000 => [6] => 100000 => 110101 => 2
00001 => [5,1] => 100001 => 110100 => 2
00010 => [4,2] => 100010 => 110111 => 3
00011 => [4,1,1] => 100011 => 110110 => 2
00100 => [3,3] => 100100 => 110001 => 3
00101 => [3,2,1] => 100101 => 110000 => 4
00110 => [3,1,2] => 100110 => 110011 => 2
00111 => [3,1,1,1] => 100111 => 110010 => 2
01000 => [2,4] => 101000 => 111101 => 4
01001 => [2,3,1] => 101001 => 111100 => 4
01010 => [2,2,2] => 101010 => 111111 => 6
01011 => [2,2,1,1] => 101011 => 111110 => 5
01100 => [2,1,3] => 101100 => 111001 => 3
01101 => [2,1,2,1] => 101101 => 111000 => 3
01110 => [2,1,1,2] => 101110 => 111011 => 3
01111 => [2,1,1,1,1] => 101111 => 111010 => 3
10000 => [1,5] => 110000 => 100101 => 2
10001 => [1,4,1] => 110001 => 100100 => 2
10010 => [1,3,2] => 110010 => 100111 => 3
10011 => [1,3,1,1] => 110011 => 100110 => 2
101001110 => [1,2,3,1,1,2] => 1101001110 => 1000011011 => ? = 4
101001111 => [1,2,3,1,1,1,1] => 1101001111 => 1000011010 => ? = 4
101010000 => [1,2,2,5] => 1101010000 => 1000000101 => ? = 6
101010010 => [1,2,2,3,2] => 1101010010 => 1000000111 => ? = 6
101010100 => [1,2,2,2,3] => 1101010100 => 1000000001 => ? = 8
101010110 => [1,2,2,2,1,2] => 1101010110 => 1000000011 => ? = 7
101011000 => [1,2,2,1,4] => 1101011000 => 1000001101 => ? = 5
101011001 => [1,2,2,1,3,1] => 1101011001 => 1000001100 => ? = 5
101011010 => [1,2,2,1,2,2] => 1101011010 => 1000001111 => ? = 5
101011100 => [1,2,2,1,1,3] => 1101011100 => ? => ? = 5
101011101 => [1,2,2,1,1,2,1] => 1101011101 => ? => ? = 5
101011110 => [1,2,2,1,1,1,2] => 1101011110 => 1000001011 => ? = 5
101100000 => [1,2,1,6] => 1101100000 => 1000110101 => ? = 3
101100001 => [1,2,1,5,1] => 1101100001 => 1000110100 => ? = 3
101100010 => [1,2,1,4,2] => 1101100010 => 1000110111 => ? = 3
101100100 => [1,2,1,3,3] => 1101100100 => 1000110001 => ? = 3
101100101 => [1,2,1,3,2,1] => 1101100101 => 1000110000 => ? = 4
101100110 => [1,2,1,3,1,2] => 1101100110 => 1000110011 => ? = 3
101101000 => [1,2,1,2,4] => 1101101000 => 1000111101 => ? = 4
101101010 => [1,2,1,2,2,2] => 1101101010 => 1000111111 => ? = 6
101101100 => [1,2,1,2,1,3] => 1101101100 => 1000111001 => ? = 3
101101101 => [1,2,1,2,1,2,1] => 1101101101 => ? => ? = 3
101101110 => [1,2,1,2,1,1,2] => 1101101110 => 1000111011 => ? = 3
101110000 => [1,2,1,1,5] => 1101110000 => 1000100101 => ? = 3
101110001 => [1,2,1,1,4,1] => 1101110001 => 1000100100 => ? = 3
101110010 => [1,2,1,1,3,2] => 1101110010 => 1000100111 => ? = 3
101110101 => [1,2,1,1,2,2,1] => 1101110101 => ? => ? = 5
101110110 => [1,2,1,1,2,1,2] => 1101110110 => 1000100011 => ? = 3
101110111 => [1,2,1,1,2,1,1,1] => 1101110111 => 1000100010 => ? = 3
101111000 => [1,2,1,1,1,4] => 1101111000 => 1000101101 => ? = 3
101111001 => [1,2,1,1,1,3,1] => 1101111001 => 1000101100 => ? = 3
101111010 => [1,2,1,1,1,2,2] => 1101111010 => 1000101111 => ? = 4
101111100 => [1,2,1,1,1,1,3] => 1101111100 => ? => ? = 3
101111101 => [1,2,1,1,1,1,2,1] => 1101111101 => 1000101000 => ? = 3
101111110 => [1,2,1,1,1,1,1,2] => 1101111110 => 1000101011 => ? = 3
101111111 => [1,2,1,1,1,1,1,1,1] => 1101111111 => 1000101010 => ? = 3
110000000 => [1,1,8] => 1110000000 => 1011010101 => ? = 2
110000010 => [1,1,6,2] => 1110000010 => 1011010111 => ? = 3
110000011 => [1,1,6,1,1] => 1110000011 => 1011010110 => ? = 2
110000101 => [1,1,5,2,1] => 1110000101 => 1011010000 => ? = 4
110000110 => [1,1,5,1,2] => 1110000110 => 1011010011 => ? = 2
110001000 => [1,1,4,4] => 1110001000 => 1011011101 => ? = 3
110001001 => [1,1,4,3,1] => 1110001001 => 1011011100 => ? = 3
110001010 => [1,1,4,2,2] => 1110001010 => 1011011111 => ? = 5
110001011 => [1,1,4,2,1,1] => 1110001011 => 1011011110 => ? = 4
110001100 => [1,1,4,1,3] => 1110001100 => 1011011001 => ? = 2
110001110 => [1,1,4,1,1,2] => 1110001110 => 1011011011 => ? = 2
110001111 => [1,1,4,1,1,1,1] => 1110001111 => ? => ? = 2
110010001 => [1,1,3,4,1] => 1110010001 => 1011000100 => ? = 3
110010010 => [1,1,3,3,2] => 1110010010 => 1011000111 => ? = 3
Description
The length of the longest constant subword.
Matching statistic: St000381
Mapping
Mp00104: Binary words —reverse⟶ Binary words
Mp00269: Binary words —flag zeros to zeros⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
St000381: Integer compositions ⟶ ℤResult quality: 79% ●values known / values provided: 79%●distinct values known / distinct values provided: 100%
Values
0 => 0 => 0 => [2] => 2
1 => 1 => 1 => [1,1] => 1
00 => 00 => 01 => [2,1] => 2
01 => 10 => 00 => [3] => 3
10 => 01 => 10 => [1,2] => 2
11 => 11 => 11 => [1,1,1] => 1
000 => 000 => 011 => [2,1,1] => 2
001 => 100 => 010 => [2,2] => 2
010 => 010 => 000 => [4] => 4
011 => 110 => 001 => [3,1] => 3
100 => 001 => 101 => [1,2,1] => 2
101 => 101 => 100 => [1,3] => 3
110 => 011 => 110 => [1,1,2] => 2
111 => 111 => 111 => [1,1,1,1] => 1
0000 => 0000 => 0111 => [2,1,1,1] => 2
0001 => 1000 => 0110 => [2,1,2] => 2
0010 => 0100 => 0100 => [2,3] => 3
0011 => 1100 => 0101 => [2,2,1] => 2
0100 => 0010 => 0001 => [4,1] => 4
0101 => 1010 => 0000 => [5] => 5
0110 => 0110 => 0010 => [3,2] => 3
0111 => 1110 => 0011 => [3,1,1] => 3
1000 => 0001 => 1011 => [1,2,1,1] => 2
1001 => 1001 => 1010 => [1,2,2] => 2
1010 => 0101 => 1000 => [1,4] => 4
1011 => 1101 => 1001 => [1,3,1] => 3
1100 => 0011 => 1101 => [1,1,2,1] => 2
1101 => 1011 => 1100 => [1,1,3] => 3
1110 => 0111 => 1110 => [1,1,1,2] => 2
1111 => 1111 => 1111 => [1,1,1,1,1] => 1
00000 => 00000 => 01111 => [2,1,1,1,1] => 2
00001 => 10000 => 01110 => [2,1,1,2] => 2
00010 => 01000 => 01100 => [2,1,3] => 3
00011 => 11000 => 01101 => [2,1,2,1] => 2
00100 => 00100 => 01001 => [2,3,1] => 3
00101 => 10100 => 01000 => [2,4] => 4
00110 => 01100 => 01010 => [2,2,2] => 2
00111 => 11100 => 01011 => [2,2,1,1] => 2
01000 => 00010 => 00011 => [4,1,1] => 4
01001 => 10010 => 00010 => [4,2] => 4
01010 => 01010 => 00000 => [6] => 6
01011 => 11010 => 00001 => [5,1] => 5
01100 => 00110 => 00101 => [3,2,1] => 3
01101 => 10110 => 00100 => [3,3] => 3
01110 => 01110 => 00110 => [3,1,2] => 3
01111 => 11110 => 00111 => [3,1,1,1] => 3
10000 => 00001 => 10111 => [1,2,1,1,1] => 2
10001 => 10001 => 10110 => [1,2,1,2] => 2
10010 => 01001 => 10100 => [1,2,3] => 3
10011 => 11001 => 10101 => [1,2,2,1] => 2
101001110 => 011100101 => 100010110 => [1,4,2,1,2] => ? = 4
101001111 => 111100101 => 100010111 => [1,4,2,1,1,1] => ? = 4
101010000 => 000010101 => 100000111 => [1,6,1,1,1] => ? = 6
101010010 => 010010101 => 100000100 => [1,6,3] => ? = 6
101010110 => 011010101 => 100000010 => [1,7,2] => ? = 7
101011000 => 000110101 => 100001011 => [1,5,2,1,1] => ? = 5
101011001 => 100110101 => 100001010 => [1,5,2,2] => ? = 5
101011010 => 010110101 => 100001000 => [1,5,4] => ? = 5
101011100 => 001110101 => 100001101 => [1,5,1,2,1] => ? = 5
101011101 => 101110101 => 100001100 => [1,5,1,3] => ? = 5
101011110 => 011110101 => 100001110 => [1,5,1,1,2] => ? = 5
101100000 => 000001101 => 100101111 => [1,3,2,1,1,1,1] => ? = 3
101100001 => 100001101 => 100101110 => [1,3,2,1,1,2] => ? = 3
101100010 => 010001101 => 100101100 => [1,3,2,1,3] => ? = 3
101100011 => 110001101 => 100101101 => [1,3,2,1,2,1] => ? = 3
101100100 => 001001101 => 100101001 => [1,3,2,3,1] => ? = 3
101100101 => 101001101 => 100101000 => [1,3,2,4] => ? = 4
101100110 => 011001101 => 100101010 => [1,3,2,2,2] => ? = 3
101101000 => 000101101 => 100100011 => [1,3,4,1,1] => ? = 4
101101001 => 100101101 => 100100010 => [1,3,4,2] => ? = 4
101101010 => 010101101 => 100100000 => [1,3,6] => ? = 6
101101100 => 001101101 => 100100101 => [1,3,3,2,1] => ? = 3
101101101 => 101101101 => 100100100 => [1,3,3,3] => ? = 3
101101110 => 011101101 => 100100110 => [1,3,3,1,2] => ? = 3
101101111 => 111101101 => 100100111 => [1,3,3,1,1,1] => ? = 3
101110000 => 000011101 => 100110111 => [1,3,1,2,1,1,1] => ? = 3
101110001 => 100011101 => 100110110 => [1,3,1,2,1,2] => ? = 3
101110010 => 010011101 => 100110100 => [1,3,1,2,3] => ? = 3
101110101 => 101011101 => 100110000 => [1,3,1,5] => ? = 5
101110110 => 011011101 => 100110010 => [1,3,1,3,2] => ? = 3
101110111 => 111011101 => 100110011 => [1,3,1,3,1,1] => ? = 3
101111000 => 000111101 => 100111011 => [1,3,1,1,2,1,1] => ? = 3
101111001 => 100111101 => 100111010 => [1,3,1,1,2,2] => ? = 3
101111010 => 010111101 => 100111000 => [1,3,1,1,4] => ? = 4
101111100 => 001111101 => 100111101 => [1,3,1,1,1,2,1] => ? = 3
101111101 => 101111101 => 100111100 => [1,3,1,1,1,3] => ? = 3
101111110 => 011111101 => 100111110 => [1,3,1,1,1,1,2] => ? = 3
101111111 => 111111101 => 100111111 => [1,3,1,1,1,1,1,1] => ? = 3
110000000 => 000000011 => 110111111 => [1,1,2,1,1,1,1,1,1] => ? = 2
110000010 => 010000011 => 110111100 => [1,1,2,1,1,1,3] => ? = 3
110000011 => 110000011 => 110111101 => [1,1,2,1,1,1,2,1] => ? = 2
110000100 => 001000011 => 110111001 => [1,1,2,1,1,3,1] => ? = 3
110000101 => 101000011 => 110111000 => [1,1,2,1,1,4] => ? = 4
110000110 => 011000011 => 110111010 => [1,1,2,1,1,2,2] => ? = 2
110001000 => 000100011 => 110110011 => [1,1,2,1,3,1,1] => ? = 3
110001001 => 100100011 => 110110010 => [1,1,2,1,3,2] => ? = 3
110001010 => 010100011 => 110110000 => [1,1,2,1,5] => ? = 5
110001011 => 110100011 => 110110001 => [1,1,2,1,4,1] => ? = 4
110001100 => 001100011 => 110110101 => [1,1,2,1,2,2,1] => ? = 2
110001110 => 011100011 => 110110110 => [1,1,2,1,2,1,2] => ? = 2
Description
The largest part of an integer composition.
Matching statistic: St001235
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
St001235: Integer compositions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 67%
Values
0 => [2] => 10 => [1,1] => 2
1 => [1,1] => 11 => [2] => 1
00 => [3] => 100 => [1,2] => 2
01 => [2,1] => 101 => [1,1,1] => 3
10 => [1,2] => 110 => [2,1] => 2
11 => [1,1,1] => 111 => [3] => 1
000 => [4] => 1000 => [1,3] => 2
001 => [3,1] => 1001 => [1,2,1] => 2
010 => [2,2] => 1010 => [1,1,1,1] => 4
011 => [2,1,1] => 1011 => [1,1,2] => 3
100 => [1,3] => 1100 => [2,2] => 2
101 => [1,2,1] => 1101 => [2,1,1] => 3
110 => [1,1,2] => 1110 => [3,1] => 2
111 => [1,1,1,1] => 1111 => [4] => 1
0000 => [5] => 10000 => [1,4] => 2
0001 => [4,1] => 10001 => [1,3,1] => 2
0010 => [3,2] => 10010 => [1,2,1,1] => 3
0011 => [3,1,1] => 10011 => [1,2,2] => 2
0100 => [2,3] => 10100 => [1,1,1,2] => 4
0101 => [2,2,1] => 10101 => [1,1,1,1,1] => 5
0110 => [2,1,2] => 10110 => [1,1,2,1] => 3
0111 => [2,1,1,1] => 10111 => [1,1,3] => 3
1000 => [1,4] => 11000 => [2,3] => 2
1001 => [1,3,1] => 11001 => [2,2,1] => 2
1010 => [1,2,2] => 11010 => [2,1,1,1] => 4
1011 => [1,2,1,1] => 11011 => [2,1,2] => 3
1100 => [1,1,3] => 11100 => [3,2] => 2
1101 => [1,1,2,1] => 11101 => [3,1,1] => 3
1110 => [1,1,1,2] => 11110 => [4,1] => 2
1111 => [1,1,1,1,1] => 11111 => [5] => 1
00000 => [6] => 100000 => [1,5] => 2
00001 => [5,1] => 100001 => [1,4,1] => 2
00010 => [4,2] => 100010 => [1,3,1,1] => 3
00011 => [4,1,1] => 100011 => [1,3,2] => 2
00100 => [3,3] => 100100 => [1,2,1,2] => 3
00101 => [3,2,1] => 100101 => [1,2,1,1,1] => 4
00110 => [3,1,2] => 100110 => [1,2,2,1] => 2
00111 => [3,1,1,1] => 100111 => [1,2,3] => 2
01000 => [2,4] => 101000 => [1,1,1,3] => 4
01001 => [2,3,1] => 101001 => [1,1,1,2,1] => 4
01010 => [2,2,2] => 101010 => [1,1,1,1,1,1] => 6
01011 => [2,2,1,1] => 101011 => [1,1,1,1,2] => 5
01100 => [2,1,3] => 101100 => [1,1,2,2] => 3
01101 => [2,1,2,1] => 101101 => [1,1,2,1,1] => 3
01110 => [2,1,1,2] => 101110 => [1,1,3,1] => 3
01111 => [2,1,1,1,1] => 101111 => [1,1,4] => 3
10000 => [1,5] => 110000 => [2,4] => 2
10001 => [1,4,1] => 110001 => [2,3,1] => 2
10010 => [1,3,2] => 110010 => [2,2,1,1] => 3
10011 => [1,3,1,1] => 110011 => [2,2,2] => 2
000000 => [7] => 1000000 => [1,6] => ? = 2
000001 => [6,1] => 1000001 => [1,5,1] => ? = 2
000010 => [5,2] => 1000010 => [1,4,1,1] => ? = 3
000011 => [5,1,1] => 1000011 => [1,4,2] => ? = 2
000100 => [4,3] => 1000100 => [1,3,1,2] => ? = 3
000101 => [4,2,1] => 1000101 => [1,3,1,1,1] => ? = 4
000110 => [4,1,2] => 1000110 => [1,3,2,1] => ? = 2
000111 => [4,1,1,1] => 1000111 => [1,3,3] => ? = 2
001000 => [3,4] => 1001000 => [1,2,1,3] => ? = 3
001001 => [3,3,1] => 1001001 => [1,2,1,2,1] => ? = 3
001010 => [3,2,2] => 1001010 => [1,2,1,1,1,1] => ? = 5
001011 => [3,2,1,1] => 1001011 => [1,2,1,1,2] => ? = 4
001100 => [3,1,3] => 1001100 => [1,2,2,2] => ? = 2
001101 => [3,1,2,1] => 1001101 => [1,2,2,1,1] => ? = 3
001110 => [3,1,1,2] => 1001110 => [1,2,3,1] => ? = 2
001111 => [3,1,1,1,1] => 1001111 => [1,2,4] => ? = 2
010000 => [2,5] => 1010000 => [1,1,1,4] => ? = 4
010001 => [2,4,1] => 1010001 => [1,1,1,3,1] => ? = 4
010010 => [2,3,2] => 1010010 => [1,1,1,2,1,1] => ? = 4
010011 => [2,3,1,1] => 1010011 => [1,1,1,2,2] => ? = 4
010100 => [2,2,3] => 1010100 => [1,1,1,1,1,2] => ? = 6
010101 => [2,2,2,1] => 1010101 => [1,1,1,1,1,1,1] => ? = 7
010110 => [2,2,1,2] => 1010110 => [1,1,1,1,2,1] => ? = 5
010111 => [2,2,1,1,1] => 1010111 => [1,1,1,1,3] => ? = 5
011000 => [2,1,4] => 1011000 => [1,1,2,3] => ? = 3
011001 => [2,1,3,1] => 1011001 => [1,1,2,2,1] => ? = 3
011010 => [2,1,2,2] => 1011010 => [1,1,2,1,1,1] => ? = 4
011011 => [2,1,2,1,1] => 1011011 => [1,1,2,1,2] => ? = 3
011100 => [2,1,1,3] => 1011100 => [1,1,3,2] => ? = 3
011101 => [2,1,1,2,1] => 1011101 => [1,1,3,1,1] => ? = 3
011110 => [2,1,1,1,2] => 1011110 => [1,1,4,1] => ? = 3
011111 => [2,1,1,1,1,1] => 1011111 => [1,1,5] => ? = 3
100000 => [1,6] => 1100000 => [2,5] => ? = 2
100001 => [1,5,1] => 1100001 => [2,4,1] => ? = 2
100010 => [1,4,2] => 1100010 => [2,3,1,1] => ? = 3
100011 => [1,4,1,1] => 1100011 => [2,3,2] => ? = 2
100100 => [1,3,3] => 1100100 => [2,2,1,2] => ? = 3
100101 => [1,3,2,1] => 1100101 => [2,2,1,1,1] => ? = 4
100110 => [1,3,1,2] => 1100110 => [2,2,2,1] => ? = 2
100111 => [1,3,1,1,1] => 1100111 => [2,2,3] => ? = 2
101000 => [1,2,4] => 1101000 => [2,1,1,3] => ? = 4
101001 => [1,2,3,1] => 1101001 => [2,1,1,2,1] => ? = 4
101010 => [1,2,2,2] => 1101010 => [2,1,1,1,1,1] => ? = 6
101011 => [1,2,2,1,1] => 1101011 => [2,1,1,1,2] => ? = 5
101100 => [1,2,1,3] => 1101100 => [2,1,2,2] => ? = 3
101101 => [1,2,1,2,1] => 1101101 => [2,1,2,1,1] => ? = 3
101110 => [1,2,1,1,2] => 1101110 => [2,1,3,1] => ? = 3
101111 => [1,2,1,1,1,1] => 1101111 => [2,1,4] => ? = 3
110000 => [1,1,5] => 1110000 => [3,4] => ? = 2
110001 => [1,1,4,1] => 1110001 => [3,3,1] => ? = 2
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".