Identifier
-
Mp00178:
Binary words
—to composition⟶
Integer compositions
St001486: Integer compositions ⟶ ℤ
Values
=>
0=>[2]=>2
1=>[1,1]=>2
00=>[3]=>2
01=>[2,1]=>3
10=>[1,2]=>3
11=>[1,1,1]=>2
000=>[4]=>2
001=>[3,1]=>3
010=>[2,2]=>4
011=>[2,1,1]=>3
100=>[1,3]=>3
101=>[1,2,1]=>4
110=>[1,1,2]=>3
111=>[1,1,1,1]=>2
0000=>[5]=>2
0001=>[4,1]=>3
0010=>[3,2]=>4
0011=>[3,1,1]=>3
0100=>[2,3]=>4
0101=>[2,2,1]=>5
0110=>[2,1,2]=>4
0111=>[2,1,1,1]=>3
1000=>[1,4]=>3
1001=>[1,3,1]=>4
1010=>[1,2,2]=>5
1011=>[1,2,1,1]=>4
1100=>[1,1,3]=>3
1101=>[1,1,2,1]=>4
1110=>[1,1,1,2]=>3
1111=>[1,1,1,1,1]=>2
00000=>[6]=>2
00001=>[5,1]=>3
00010=>[4,2]=>4
00011=>[4,1,1]=>3
00100=>[3,3]=>4
00101=>[3,2,1]=>5
00110=>[3,1,2]=>4
00111=>[3,1,1,1]=>3
01000=>[2,4]=>4
01001=>[2,3,1]=>5
01010=>[2,2,2]=>6
01011=>[2,2,1,1]=>5
01100=>[2,1,3]=>4
01101=>[2,1,2,1]=>5
01110=>[2,1,1,2]=>4
01111=>[2,1,1,1,1]=>3
10000=>[1,5]=>3
10001=>[1,4,1]=>4
10010=>[1,3,2]=>5
10011=>[1,3,1,1]=>4
10100=>[1,2,3]=>5
10101=>[1,2,2,1]=>6
10110=>[1,2,1,2]=>5
10111=>[1,2,1,1,1]=>4
11000=>[1,1,4]=>3
11001=>[1,1,3,1]=>4
11010=>[1,1,2,2]=>5
11011=>[1,1,2,1,1]=>4
11100=>[1,1,1,3]=>3
11101=>[1,1,1,2,1]=>4
11110=>[1,1,1,1,2]=>3
11111=>[1,1,1,1,1,1]=>2
000000=>[7]=>2
000001=>[6,1]=>3
000010=>[5,2]=>4
000011=>[5,1,1]=>3
000100=>[4,3]=>4
000101=>[4,2,1]=>5
000110=>[4,1,2]=>4
000111=>[4,1,1,1]=>3
001000=>[3,4]=>4
001001=>[3,3,1]=>5
001010=>[3,2,2]=>6
001011=>[3,2,1,1]=>5
001100=>[3,1,3]=>4
001101=>[3,1,2,1]=>5
001110=>[3,1,1,2]=>4
001111=>[3,1,1,1,1]=>3
010000=>[2,5]=>4
010001=>[2,4,1]=>5
010010=>[2,3,2]=>6
010011=>[2,3,1,1]=>5
010100=>[2,2,3]=>6
010101=>[2,2,2,1]=>7
010110=>[2,2,1,2]=>6
010111=>[2,2,1,1,1]=>5
011000=>[2,1,4]=>4
011001=>[2,1,3,1]=>5
011010=>[2,1,2,2]=>6
011011=>[2,1,2,1,1]=>5
011100=>[2,1,1,3]=>4
011101=>[2,1,1,2,1]=>5
011110=>[2,1,1,1,2]=>4
011111=>[2,1,1,1,1,1]=>3
100000=>[1,6]=>3
100001=>[1,5,1]=>4
100010=>[1,4,2]=>5
100011=>[1,4,1,1]=>4
100100=>[1,3,3]=>5
100101=>[1,3,2,1]=>6
100110=>[1,3,1,2]=>5
100111=>[1,3,1,1,1]=>4
101000=>[1,2,4]=>5
101001=>[1,2,3,1]=>6
101010=>[1,2,2,2]=>7
101011=>[1,2,2,1,1]=>6
101100=>[1,2,1,3]=>5
101101=>[1,2,1,2,1]=>6
101110=>[1,2,1,1,2]=>5
101111=>[1,2,1,1,1,1]=>4
110000=>[1,1,5]=>3
110001=>[1,1,4,1]=>4
110010=>[1,1,3,2]=>5
110011=>[1,1,3,1,1]=>4
110100=>[1,1,2,3]=>5
110101=>[1,1,2,2,1]=>6
110110=>[1,1,2,1,2]=>5
110111=>[1,1,2,1,1,1]=>4
111000=>[1,1,1,4]=>3
111001=>[1,1,1,3,1]=>4
111010=>[1,1,1,2,2]=>5
111011=>[1,1,1,2,1,1]=>4
111100=>[1,1,1,1,3]=>3
111101=>[1,1,1,1,2,1]=>4
111110=>[1,1,1,1,1,2]=>3
111111=>[1,1,1,1,1,1,1]=>2
0000000=>[8]=>2
0000001=>[7,1]=>3
0000010=>[6,2]=>4
0000011=>[6,1,1]=>3
0000100=>[5,3]=>4
0000101=>[5,2,1]=>5
0000110=>[5,1,2]=>4
0000111=>[5,1,1,1]=>3
0001000=>[4,4]=>4
0001001=>[4,3,1]=>5
0001010=>[4,2,2]=>6
0001011=>[4,2,1,1]=>5
0001100=>[4,1,3]=>4
0001101=>[4,1,2,1]=>5
0001110=>[4,1,1,2]=>4
0001111=>[4,1,1,1,1]=>3
0010000=>[3,5]=>4
0010001=>[3,4,1]=>5
0010010=>[3,3,2]=>6
0010011=>[3,3,1,1]=>5
0010100=>[3,2,3]=>6
0010101=>[3,2,2,1]=>7
0010110=>[3,2,1,2]=>6
0010111=>[3,2,1,1,1]=>5
0011000=>[3,1,4]=>4
0011001=>[3,1,3,1]=>5
0011010=>[3,1,2,2]=>6
0011011=>[3,1,2,1,1]=>5
0011100=>[3,1,1,3]=>4
0011101=>[3,1,1,2,1]=>5
0011110=>[3,1,1,1,2]=>4
0011111=>[3,1,1,1,1,1]=>3
0100000=>[2,6]=>4
0100001=>[2,5,1]=>5
0100010=>[2,4,2]=>6
0100011=>[2,4,1,1]=>5
0100100=>[2,3,3]=>6
0100101=>[2,3,2,1]=>7
0100110=>[2,3,1,2]=>6
0100111=>[2,3,1,1,1]=>5
0101000=>[2,2,4]=>6
0101001=>[2,2,3,1]=>7
0101010=>[2,2,2,2]=>8
0101011=>[2,2,2,1,1]=>7
0101100=>[2,2,1,3]=>6
0101101=>[2,2,1,2,1]=>7
0101110=>[2,2,1,1,2]=>6
0101111=>[2,2,1,1,1,1]=>5
0110000=>[2,1,5]=>4
0110001=>[2,1,4,1]=>5
0110010=>[2,1,3,2]=>6
0110011=>[2,1,3,1,1]=>5
0110100=>[2,1,2,3]=>6
0110101=>[2,1,2,2,1]=>7
0110110=>[2,1,2,1,2]=>6
0110111=>[2,1,2,1,1,1]=>5
0111000=>[2,1,1,4]=>4
0111001=>[2,1,1,3,1]=>5
0111010=>[2,1,1,2,2]=>6
0111011=>[2,1,1,2,1,1]=>5
0111100=>[2,1,1,1,3]=>4
0111101=>[2,1,1,1,2,1]=>5
0111110=>[2,1,1,1,1,2]=>4
0111111=>[2,1,1,1,1,1,1]=>3
1000000=>[1,7]=>3
1000001=>[1,6,1]=>4
1000010=>[1,5,2]=>5
1000011=>[1,5,1,1]=>4
1000100=>[1,4,3]=>5
1000101=>[1,4,2,1]=>6
1000110=>[1,4,1,2]=>5
1000111=>[1,4,1,1,1]=>4
1001000=>[1,3,4]=>5
1001001=>[1,3,3,1]=>6
1001010=>[1,3,2,2]=>7
1001011=>[1,3,2,1,1]=>6
1001100=>[1,3,1,3]=>5
1001101=>[1,3,1,2,1]=>6
1001110=>[1,3,1,1,2]=>5
1001111=>[1,3,1,1,1,1]=>4
1010000=>[1,2,5]=>5
1010001=>[1,2,4,1]=>6
1010010=>[1,2,3,2]=>7
1010011=>[1,2,3,1,1]=>6
1010100=>[1,2,2,3]=>7
1010101=>[1,2,2,2,1]=>8
1010110=>[1,2,2,1,2]=>7
1010111=>[1,2,2,1,1,1]=>6
1011000=>[1,2,1,4]=>5
1011001=>[1,2,1,3,1]=>6
1011010=>[1,2,1,2,2]=>7
1011011=>[1,2,1,2,1,1]=>6
1011100=>[1,2,1,1,3]=>5
1011101=>[1,2,1,1,2,1]=>6
1011110=>[1,2,1,1,1,2]=>5
1011111=>[1,2,1,1,1,1,1]=>4
1100000=>[1,1,6]=>3
1100001=>[1,1,5,1]=>4
1100010=>[1,1,4,2]=>5
1100011=>[1,1,4,1,1]=>4
1100100=>[1,1,3,3]=>5
1100101=>[1,1,3,2,1]=>6
1100110=>[1,1,3,1,2]=>5
1100111=>[1,1,3,1,1,1]=>4
1101000=>[1,1,2,4]=>5
1101001=>[1,1,2,3,1]=>6
1101010=>[1,1,2,2,2]=>7
1101011=>[1,1,2,2,1,1]=>6
1101100=>[1,1,2,1,3]=>5
1101101=>[1,1,2,1,2,1]=>6
1101110=>[1,1,2,1,1,2]=>5
1101111=>[1,1,2,1,1,1,1]=>4
1110000=>[1,1,1,5]=>3
1110001=>[1,1,1,4,1]=>4
1110010=>[1,1,1,3,2]=>5
1110011=>[1,1,1,3,1,1]=>4
1110100=>[1,1,1,2,3]=>5
1110101=>[1,1,1,2,2,1]=>6
1110110=>[1,1,1,2,1,2]=>5
1110111=>[1,1,1,2,1,1,1]=>4
1111000=>[1,1,1,1,4]=>3
1111001=>[1,1,1,1,3,1]=>4
1111010=>[1,1,1,1,2,2]=>5
1111011=>[1,1,1,1,2,1,1]=>4
1111100=>[1,1,1,1,1,3]=>3
1111101=>[1,1,1,1,1,2,1]=>4
1111110=>[1,1,1,1,1,1,2]=>3
1111111=>[1,1,1,1,1,1,1,1]=>2
00000000=>[9]=>2
00000001=>[8,1]=>3
00000010=>[7,2]=>4
00000011=>[7,1,1]=>3
00000100=>[6,3]=>4
00000101=>[6,2,1]=>5
00000110=>[6,1,2]=>4
00000111=>[6,1,1,1]=>3
00001000=>[5,4]=>4
00001001=>[5,3,1]=>5
00001010=>[5,2,2]=>6
00001011=>[5,2,1,1]=>5
00001100=>[5,1,3]=>4
00001101=>[5,1,2,1]=>5
00001110=>[5,1,1,2]=>4
00001111=>[5,1,1,1,1]=>3
00010000=>[4,5]=>4
00010001=>[4,4,1]=>5
00010010=>[4,3,2]=>6
00010011=>[4,3,1,1]=>5
00010100=>[4,2,3]=>6
00010101=>[4,2,2,1]=>7
00010110=>[4,2,1,2]=>6
00010111=>[4,2,1,1,1]=>5
00011000=>[4,1,4]=>4
00011001=>[4,1,3,1]=>5
00011010=>[4,1,2,2]=>6
00011011=>[4,1,2,1,1]=>5
00011100=>[4,1,1,3]=>4
00011101=>[4,1,1,2,1]=>5
00011110=>[4,1,1,1,2]=>4
00011111=>[4,1,1,1,1,1]=>3
00100000=>[3,6]=>4
00100001=>[3,5,1]=>5
00100010=>[3,4,2]=>6
00100011=>[3,4,1,1]=>5
00100100=>[3,3,3]=>6
00100101=>[3,3,2,1]=>7
00100110=>[3,3,1,2]=>6
00100111=>[3,3,1,1,1]=>5
00101000=>[3,2,4]=>6
00101001=>[3,2,3,1]=>7
00101010=>[3,2,2,2]=>8
00101011=>[3,2,2,1,1]=>7
00101100=>[3,2,1,3]=>6
00101101=>[3,2,1,2,1]=>7
00101110=>[3,2,1,1,2]=>6
00101111=>[3,2,1,1,1,1]=>5
00110000=>[3,1,5]=>4
00110001=>[3,1,4,1]=>5
00110010=>[3,1,3,2]=>6
00110011=>[3,1,3,1,1]=>5
00110100=>[3,1,2,3]=>6
00110101=>[3,1,2,2,1]=>7
00110110=>[3,1,2,1,2]=>6
00110111=>[3,1,2,1,1,1]=>5
00111000=>[3,1,1,4]=>4
00111001=>[3,1,1,3,1]=>5
00111010=>[3,1,1,2,2]=>6
00111011=>[3,1,1,2,1,1]=>5
00111100=>[3,1,1,1,3]=>4
00111101=>[3,1,1,1,2,1]=>5
00111110=>[3,1,1,1,1,2]=>4
00111111=>[3,1,1,1,1,1,1]=>3
01000000=>[2,7]=>4
01000001=>[2,6,1]=>5
01000010=>[2,5,2]=>6
01000011=>[2,5,1,1]=>5
01000100=>[2,4,3]=>6
01000101=>[2,4,2,1]=>7
01000110=>[2,4,1,2]=>6
01000111=>[2,4,1,1,1]=>5
01001000=>[2,3,4]=>6
01001001=>[2,3,3,1]=>7
01001010=>[2,3,2,2]=>8
01001011=>[2,3,2,1,1]=>7
01001100=>[2,3,1,3]=>6
01001101=>[2,3,1,2,1]=>7
01001110=>[2,3,1,1,2]=>6
01001111=>[2,3,1,1,1,1]=>5
01010000=>[2,2,5]=>6
01010001=>[2,2,4,1]=>7
01010010=>[2,2,3,2]=>8
01010011=>[2,2,3,1,1]=>7
01010100=>[2,2,2,3]=>8
01010101=>[2,2,2,2,1]=>9
01010110=>[2,2,2,1,2]=>8
01010111=>[2,2,2,1,1,1]=>7
01011000=>[2,2,1,4]=>6
01011001=>[2,2,1,3,1]=>7
01011010=>[2,2,1,2,2]=>8
01011011=>[2,2,1,2,1,1]=>7
01011100=>[2,2,1,1,3]=>6
01011101=>[2,2,1,1,2,1]=>7
01011110=>[2,2,1,1,1,2]=>6
01011111=>[2,2,1,1,1,1,1]=>5
01100000=>[2,1,6]=>4
01100001=>[2,1,5,1]=>5
01100010=>[2,1,4,2]=>6
01100011=>[2,1,4,1,1]=>5
01100100=>[2,1,3,3]=>6
01100101=>[2,1,3,2,1]=>7
01100110=>[2,1,3,1,2]=>6
01100111=>[2,1,3,1,1,1]=>5
01101000=>[2,1,2,4]=>6
01101001=>[2,1,2,3,1]=>7
01101010=>[2,1,2,2,2]=>8
01101011=>[2,1,2,2,1,1]=>7
01101100=>[2,1,2,1,3]=>6
01101101=>[2,1,2,1,2,1]=>7
01101110=>[2,1,2,1,1,2]=>6
01101111=>[2,1,2,1,1,1,1]=>5
01110000=>[2,1,1,5]=>4
01110001=>[2,1,1,4,1]=>5
01110010=>[2,1,1,3,2]=>6
01110011=>[2,1,1,3,1,1]=>5
01110100=>[2,1,1,2,3]=>6
01110101=>[2,1,1,2,2,1]=>7
01110110=>[2,1,1,2,1,2]=>6
01110111=>[2,1,1,2,1,1,1]=>5
01111000=>[2,1,1,1,4]=>4
01111001=>[2,1,1,1,3,1]=>5
01111010=>[2,1,1,1,2,2]=>6
01111011=>[2,1,1,1,2,1,1]=>5
01111100=>[2,1,1,1,1,3]=>4
01111101=>[2,1,1,1,1,2,1]=>5
01111110=>[2,1,1,1,1,1,2]=>4
01111111=>[2,1,1,1,1,1,1,1]=>3
10000000=>[1,8]=>3
10000001=>[1,7,1]=>4
10000010=>[1,6,2]=>5
10000011=>[1,6,1,1]=>4
10000100=>[1,5,3]=>5
10000101=>[1,5,2,1]=>6
10000110=>[1,5,1,2]=>5
10000111=>[1,5,1,1,1]=>4
10001000=>[1,4,4]=>5
10001001=>[1,4,3,1]=>6
10001010=>[1,4,2,2]=>7
10001011=>[1,4,2,1,1]=>6
10001100=>[1,4,1,3]=>5
10001101=>[1,4,1,2,1]=>6
10001110=>[1,4,1,1,2]=>5
10001111=>[1,4,1,1,1,1]=>4
10010000=>[1,3,5]=>5
10010001=>[1,3,4,1]=>6
10010010=>[1,3,3,2]=>7
10010011=>[1,3,3,1,1]=>6
10010100=>[1,3,2,3]=>7
10010101=>[1,3,2,2,1]=>8
10010110=>[1,3,2,1,2]=>7
10010111=>[1,3,2,1,1,1]=>6
10011000=>[1,3,1,4]=>5
10011001=>[1,3,1,3,1]=>6
10011010=>[1,3,1,2,2]=>7
10011011=>[1,3,1,2,1,1]=>6
10011100=>[1,3,1,1,3]=>5
10011101=>[1,3,1,1,2,1]=>6
10011110=>[1,3,1,1,1,2]=>5
10011111=>[1,3,1,1,1,1,1]=>4
10100000=>[1,2,6]=>5
10100001=>[1,2,5,1]=>6
10100010=>[1,2,4,2]=>7
10100011=>[1,2,4,1,1]=>6
10100100=>[1,2,3,3]=>7
10100101=>[1,2,3,2,1]=>8
10100110=>[1,2,3,1,2]=>7
10100111=>[1,2,3,1,1,1]=>6
10101000=>[1,2,2,4]=>7
10101001=>[1,2,2,3,1]=>8
10101010=>[1,2,2,2,2]=>9
10101011=>[1,2,2,2,1,1]=>8
10101100=>[1,2,2,1,3]=>7
10101101=>[1,2,2,1,2,1]=>8
10101110=>[1,2,2,1,1,2]=>7
10101111=>[1,2,2,1,1,1,1]=>6
10110000=>[1,2,1,5]=>5
10110001=>[1,2,1,4,1]=>6
10110010=>[1,2,1,3,2]=>7
10110011=>[1,2,1,3,1,1]=>6
10110100=>[1,2,1,2,3]=>7
10110101=>[1,2,1,2,2,1]=>8
10110110=>[1,2,1,2,1,2]=>7
10110111=>[1,2,1,2,1,1,1]=>6
10111000=>[1,2,1,1,4]=>5
10111001=>[1,2,1,1,3,1]=>6
10111010=>[1,2,1,1,2,2]=>7
10111011=>[1,2,1,1,2,1,1]=>6
10111100=>[1,2,1,1,1,3]=>5
10111101=>[1,2,1,1,1,2,1]=>6
10111110=>[1,2,1,1,1,1,2]=>5
10111111=>[1,2,1,1,1,1,1,1]=>4
11000000=>[1,1,7]=>3
11000001=>[1,1,6,1]=>4
11000010=>[1,1,5,2]=>5
11000011=>[1,1,5,1,1]=>4
11000100=>[1,1,4,3]=>5
11000101=>[1,1,4,2,1]=>6
11000110=>[1,1,4,1,2]=>5
11000111=>[1,1,4,1,1,1]=>4
11001000=>[1,1,3,4]=>5
11001001=>[1,1,3,3,1]=>6
11001010=>[1,1,3,2,2]=>7
11001011=>[1,1,3,2,1,1]=>6
11001100=>[1,1,3,1,3]=>5
11001101=>[1,1,3,1,2,1]=>6
11001110=>[1,1,3,1,1,2]=>5
11001111=>[1,1,3,1,1,1,1]=>4
11010000=>[1,1,2,5]=>5
11010001=>[1,1,2,4,1]=>6
11010010=>[1,1,2,3,2]=>7
11010011=>[1,1,2,3,1,1]=>6
11010100=>[1,1,2,2,3]=>7
11010101=>[1,1,2,2,2,1]=>8
11010110=>[1,1,2,2,1,2]=>7
11010111=>[1,1,2,2,1,1,1]=>6
11011000=>[1,1,2,1,4]=>5
11011001=>[1,1,2,1,3,1]=>6
11011010=>[1,1,2,1,2,2]=>7
11011011=>[1,1,2,1,2,1,1]=>6
11011100=>[1,1,2,1,1,3]=>5
11011101=>[1,1,2,1,1,2,1]=>6
11011110=>[1,1,2,1,1,1,2]=>5
11011111=>[1,1,2,1,1,1,1,1]=>4
11100000=>[1,1,1,6]=>3
11100001=>[1,1,1,5,1]=>4
11100010=>[1,1,1,4,2]=>5
11100011=>[1,1,1,4,1,1]=>4
11100100=>[1,1,1,3,3]=>5
11100101=>[1,1,1,3,2,1]=>6
11100110=>[1,1,1,3,1,2]=>5
11100111=>[1,1,1,3,1,1,1]=>4
11101000=>[1,1,1,2,4]=>5
11101001=>[1,1,1,2,3,1]=>6
11101010=>[1,1,1,2,2,2]=>7
11101011=>[1,1,1,2,2,1,1]=>6
11101100=>[1,1,1,2,1,3]=>5
11101101=>[1,1,1,2,1,2,1]=>6
11101110=>[1,1,1,2,1,1,2]=>5
11101111=>[1,1,1,2,1,1,1,1]=>4
11110000=>[1,1,1,1,5]=>3
11110001=>[1,1,1,1,4,1]=>4
11110010=>[1,1,1,1,3,2]=>5
11110011=>[1,1,1,1,3,1,1]=>4
11110100=>[1,1,1,1,2,3]=>5
11110101=>[1,1,1,1,2,2,1]=>6
11110110=>[1,1,1,1,2,1,2]=>5
11110111=>[1,1,1,1,2,1,1,1]=>4
11111000=>[1,1,1,1,1,4]=>3
11111001=>[1,1,1,1,1,3,1]=>4
11111010=>[1,1,1,1,1,2,2]=>5
11111011=>[1,1,1,1,1,2,1,1]=>4
11111100=>[1,1,1,1,1,1,3]=>3
11111101=>[1,1,1,1,1,1,2,1]=>4
11111110=>[1,1,1,1,1,1,1,2]=>3
11111111=>[1,1,1,1,1,1,1,1,1]=>2
000000000=>[10]=>2
000000001=>[9,1]=>3
000000010=>[8,2]=>4
000000011=>[8,1,1]=>3
000000100=>[7,3]=>4
000000101=>[7,2,1]=>5
000000110=>[7,1,2]=>4
000000111=>[7,1,1,1]=>3
000001000=>[6,4]=>4
000001001=>[6,3,1]=>5
000001010=>[6,2,2]=>6
000001011=>[6,2,1,1]=>5
000001100=>[6,1,3]=>4
000001101=>[6,1,2,1]=>5
000001110=>[6,1,1,2]=>4
000001111=>[6,1,1,1,1]=>3
000010000=>[5,5]=>4
000010001=>[5,4,1]=>5
000010010=>[5,3,2]=>6
000010011=>[5,3,1,1]=>5
000010100=>[5,2,3]=>6
000010101=>[5,2,2,1]=>7
000010110=>[5,2,1,2]=>6
000010111=>[5,2,1,1,1]=>5
000011000=>[5,1,4]=>4
000011001=>[5,1,3,1]=>5
000011010=>[5,1,2,2]=>6
000011011=>[5,1,2,1,1]=>5
000011100=>[5,1,1,3]=>4
000011101=>[5,1,1,2,1]=>5
000011110=>[5,1,1,1,2]=>4
000011111=>[5,1,1,1,1,1]=>3
000100000=>[4,6]=>4
000100001=>[4,5,1]=>5
000100010=>[4,4,2]=>6
000100011=>[4,4,1,1]=>5
000100100=>[4,3,3]=>6
000100101=>[4,3,2,1]=>7
000100110=>[4,3,1,2]=>6
000100111=>[4,3,1,1,1]=>5
000101000=>[4,2,4]=>6
000101001=>[4,2,3,1]=>7
000101010=>[4,2,2,2]=>8
000101011=>[4,2,2,1,1]=>7
000101100=>[4,2,1,3]=>6
000101101=>[4,2,1,2,1]=>7
000101110=>[4,2,1,1,2]=>6
000101111=>[4,2,1,1,1,1]=>5
000110000=>[4,1,5]=>4
000110001=>[4,1,4,1]=>5
000110010=>[4,1,3,2]=>6
000110011=>[4,1,3,1,1]=>5
000110100=>[4,1,2,3]=>6
000110101=>[4,1,2,2,1]=>7
000110110=>[4,1,2,1,2]=>6
000110111=>[4,1,2,1,1,1]=>5
000111000=>[4,1,1,4]=>4
000111001=>[4,1,1,3,1]=>5
000111010=>[4,1,1,2,2]=>6
000111011=>[4,1,1,2,1,1]=>5
000111100=>[4,1,1,1,3]=>4
000111101=>[4,1,1,1,2,1]=>5
000111110=>[4,1,1,1,1,2]=>4
000111111=>[4,1,1,1,1,1,1]=>3
001000000=>[3,7]=>4
001000001=>[3,6,1]=>5
001000010=>[3,5,2]=>6
001000011=>[3,5,1,1]=>5
001000100=>[3,4,3]=>6
001000101=>[3,4,2,1]=>7
001000110=>[3,4,1,2]=>6
001000111=>[3,4,1,1,1]=>5
001001000=>[3,3,4]=>6
001001001=>[3,3,3,1]=>7
001001010=>[3,3,2,2]=>8
001001011=>[3,3,2,1,1]=>7
001001100=>[3,3,1,3]=>6
001001101=>[3,3,1,2,1]=>7
001001110=>[3,3,1,1,2]=>6
001001111=>[3,3,1,1,1,1]=>5
001010000=>[3,2,5]=>6
001010001=>[3,2,4,1]=>7
001010010=>[3,2,3,2]=>8
001010011=>[3,2,3,1,1]=>7
001010100=>[3,2,2,3]=>8
001010101=>[3,2,2,2,1]=>9
001010110=>[3,2,2,1,2]=>8
001010111=>[3,2,2,1,1,1]=>7
001011000=>[3,2,1,4]=>6
001011001=>[3,2,1,3,1]=>7
001011010=>[3,2,1,2,2]=>8
001011011=>[3,2,1,2,1,1]=>7
001011100=>[3,2,1,1,3]=>6
001011101=>[3,2,1,1,2,1]=>7
001011110=>[3,2,1,1,1,2]=>6
001011111=>[3,2,1,1,1,1,1]=>5
001100000=>[3,1,6]=>4
001100001=>[3,1,5,1]=>5
001100010=>[3,1,4,2]=>6
001100011=>[3,1,4,1,1]=>5
001100100=>[3,1,3,3]=>6
001100101=>[3,1,3,2,1]=>7
001100110=>[3,1,3,1,2]=>6
001100111=>[3,1,3,1,1,1]=>5
001101000=>[3,1,2,4]=>6
001101001=>[3,1,2,3,1]=>7
001101010=>[3,1,2,2,2]=>8
001101011=>[3,1,2,2,1,1]=>7
001101100=>[3,1,2,1,3]=>6
001101101=>[3,1,2,1,2,1]=>7
001101110=>[3,1,2,1,1,2]=>6
001101111=>[3,1,2,1,1,1,1]=>5
001110000=>[3,1,1,5]=>4
001110001=>[3,1,1,4,1]=>5
001110010=>[3,1,1,3,2]=>6
001110011=>[3,1,1,3,1,1]=>5
001110100=>[3,1,1,2,3]=>6
001110101=>[3,1,1,2,2,1]=>7
001110110=>[3,1,1,2,1,2]=>6
001110111=>[3,1,1,2,1,1,1]=>5
001111000=>[3,1,1,1,4]=>4
001111001=>[3,1,1,1,3,1]=>5
001111010=>[3,1,1,1,2,2]=>6
001111011=>[3,1,1,1,2,1,1]=>5
001111100=>[3,1,1,1,1,3]=>4
001111101=>[3,1,1,1,1,2,1]=>5
001111110=>[3,1,1,1,1,1,2]=>4
001111111=>[3,1,1,1,1,1,1,1]=>3
010000000=>[2,8]=>4
010000001=>[2,7,1]=>5
010000010=>[2,6,2]=>6
010000011=>[2,6,1,1]=>5
010000100=>[2,5,3]=>6
010000101=>[2,5,2,1]=>7
010000110=>[2,5,1,2]=>6
010000111=>[2,5,1,1,1]=>5
010001000=>[2,4,4]=>6
010001001=>[2,4,3,1]=>7
010001010=>[2,4,2,2]=>8
010001011=>[2,4,2,1,1]=>7
010001100=>[2,4,1,3]=>6
010001101=>[2,4,1,2,1]=>7
010001110=>[2,4,1,1,2]=>6
010001111=>[2,4,1,1,1,1]=>5
010010000=>[2,3,5]=>6
010010001=>[2,3,4,1]=>7
010010010=>[2,3,3,2]=>8
010010011=>[2,3,3,1,1]=>7
010010100=>[2,3,2,3]=>8
010010101=>[2,3,2,2,1]=>9
010010110=>[2,3,2,1,2]=>8
010010111=>[2,3,2,1,1,1]=>7
010011000=>[2,3,1,4]=>6
010011001=>[2,3,1,3,1]=>7
010011010=>[2,3,1,2,2]=>8
010011011=>[2,3,1,2,1,1]=>7
010011100=>[2,3,1,1,3]=>6
010011101=>[2,3,1,1,2,1]=>7
010011110=>[2,3,1,1,1,2]=>6
010011111=>[2,3,1,1,1,1,1]=>5
010100000=>[2,2,6]=>6
010100001=>[2,2,5,1]=>7
010100010=>[2,2,4,2]=>8
010100011=>[2,2,4,1,1]=>7
010100100=>[2,2,3,3]=>8
010100101=>[2,2,3,2,1]=>9
010100110=>[2,2,3,1,2]=>8
010100111=>[2,2,3,1,1,1]=>7
010101000=>[2,2,2,4]=>8
010101001=>[2,2,2,3,1]=>9
010101010=>[2,2,2,2,2]=>10
010101011=>[2,2,2,2,1,1]=>9
010101100=>[2,2,2,1,3]=>8
010101101=>[2,2,2,1,2,1]=>9
010101110=>[2,2,2,1,1,2]=>8
010101111=>[2,2,2,1,1,1,1]=>7
010110000=>[2,2,1,5]=>6
010110001=>[2,2,1,4,1]=>7
010110010=>[2,2,1,3,2]=>8
010110011=>[2,2,1,3,1,1]=>7
010110100=>[2,2,1,2,3]=>8
010110101=>[2,2,1,2,2,1]=>9
010110110=>[2,2,1,2,1,2]=>8
010110111=>[2,2,1,2,1,1,1]=>7
010111000=>[2,2,1,1,4]=>6
010111001=>[2,2,1,1,3,1]=>7
010111010=>[2,2,1,1,2,2]=>8
010111011=>[2,2,1,1,2,1,1]=>7
010111100=>[2,2,1,1,1,3]=>6
010111101=>[2,2,1,1,1,2,1]=>7
010111110=>[2,2,1,1,1,1,2]=>6
010111111=>[2,2,1,1,1,1,1,1]=>5
011000000=>[2,1,7]=>4
011000001=>[2,1,6,1]=>5
011000010=>[2,1,5,2]=>6
011000011=>[2,1,5,1,1]=>5
011000100=>[2,1,4,3]=>6
011000101=>[2,1,4,2,1]=>7
011000110=>[2,1,4,1,2]=>6
011000111=>[2,1,4,1,1,1]=>5
011001000=>[2,1,3,4]=>6
011001001=>[2,1,3,3,1]=>7
011001010=>[2,1,3,2,2]=>8
011001011=>[2,1,3,2,1,1]=>7
011001100=>[2,1,3,1,3]=>6
011001101=>[2,1,3,1,2,1]=>7
011001110=>[2,1,3,1,1,2]=>6
011001111=>[2,1,3,1,1,1,1]=>5
011010000=>[2,1,2,5]=>6
011010001=>[2,1,2,4,1]=>7
011010010=>[2,1,2,3,2]=>8
011010011=>[2,1,2,3,1,1]=>7
011010100=>[2,1,2,2,3]=>8
011010101=>[2,1,2,2,2,1]=>9
011010110=>[2,1,2,2,1,2]=>8
011010111=>[2,1,2,2,1,1,1]=>7
011011000=>[2,1,2,1,4]=>6
011011001=>[2,1,2,1,3,1]=>7
011011010=>[2,1,2,1,2,2]=>8
011011011=>[2,1,2,1,2,1,1]=>7
011011100=>[2,1,2,1,1,3]=>6
011011101=>[2,1,2,1,1,2,1]=>7
011011110=>[2,1,2,1,1,1,2]=>6
011011111=>[2,1,2,1,1,1,1,1]=>5
011100000=>[2,1,1,6]=>4
011100001=>[2,1,1,5,1]=>5
011100010=>[2,1,1,4,2]=>6
011100011=>[2,1,1,4,1,1]=>5
011100100=>[2,1,1,3,3]=>6
011100101=>[2,1,1,3,2,1]=>7
011100110=>[2,1,1,3,1,2]=>6
011100111=>[2,1,1,3,1,1,1]=>5
011101000=>[2,1,1,2,4]=>6
011101001=>[2,1,1,2,3,1]=>7
011101010=>[2,1,1,2,2,2]=>8
011101011=>[2,1,1,2,2,1,1]=>7
011101100=>[2,1,1,2,1,3]=>6
011101101=>[2,1,1,2,1,2,1]=>7
011101110=>[2,1,1,2,1,1,2]=>6
011101111=>[2,1,1,2,1,1,1,1]=>5
011110000=>[2,1,1,1,5]=>4
011110001=>[2,1,1,1,4,1]=>5
011110010=>[2,1,1,1,3,2]=>6
011110011=>[2,1,1,1,3,1,1]=>5
011110100=>[2,1,1,1,2,3]=>6
011110101=>[2,1,1,1,2,2,1]=>7
011110110=>[2,1,1,1,2,1,2]=>6
011110111=>[2,1,1,1,2,1,1,1]=>5
011111000=>[2,1,1,1,1,4]=>4
011111001=>[2,1,1,1,1,3,1]=>5
011111010=>[2,1,1,1,1,2,2]=>6
011111011=>[2,1,1,1,1,2,1,1]=>5
011111100=>[2,1,1,1,1,1,3]=>4
011111101=>[2,1,1,1,1,1,2,1]=>5
011111110=>[2,1,1,1,1,1,1,2]=>4
011111111=>[2,1,1,1,1,1,1,1,1]=>3
100000000=>[1,9]=>3
100000001=>[1,8,1]=>4
100000010=>[1,7,2]=>5
100000011=>[1,7,1,1]=>4
100000100=>[1,6,3]=>5
100000101=>[1,6,2,1]=>6
100000110=>[1,6,1,2]=>5
100000111=>[1,6,1,1,1]=>4
100001000=>[1,5,4]=>5
100001001=>[1,5,3,1]=>6
100001010=>[1,5,2,2]=>7
100001011=>[1,5,2,1,1]=>6
100001100=>[1,5,1,3]=>5
100001101=>[1,5,1,2,1]=>6
100001110=>[1,5,1,1,2]=>5
100001111=>[1,5,1,1,1,1]=>4
100010000=>[1,4,5]=>5
100010001=>[1,4,4,1]=>6
100010010=>[1,4,3,2]=>7
100010011=>[1,4,3,1,1]=>6
100010100=>[1,4,2,3]=>7
100010101=>[1,4,2,2,1]=>8
100010110=>[1,4,2,1,2]=>7
100010111=>[1,4,2,1,1,1]=>6
100011000=>[1,4,1,4]=>5
100011001=>[1,4,1,3,1]=>6
100011010=>[1,4,1,2,2]=>7
100011011=>[1,4,1,2,1,1]=>6
100011100=>[1,4,1,1,3]=>5
100011101=>[1,4,1,1,2,1]=>6
100011110=>[1,4,1,1,1,2]=>5
100011111=>[1,4,1,1,1,1,1]=>4
100100000=>[1,3,6]=>5
100100001=>[1,3,5,1]=>6
100100010=>[1,3,4,2]=>7
100100011=>[1,3,4,1,1]=>6
100100100=>[1,3,3,3]=>7
100100101=>[1,3,3,2,1]=>8
100100110=>[1,3,3,1,2]=>7
100100111=>[1,3,3,1,1,1]=>6
100101000=>[1,3,2,4]=>7
100101001=>[1,3,2,3,1]=>8
100101010=>[1,3,2,2,2]=>9
100101011=>[1,3,2,2,1,1]=>8
100101100=>[1,3,2,1,3]=>7
100101101=>[1,3,2,1,2,1]=>8
100101110=>[1,3,2,1,1,2]=>7
100101111=>[1,3,2,1,1,1,1]=>6
100110000=>[1,3,1,5]=>5
100110001=>[1,3,1,4,1]=>6
100110010=>[1,3,1,3,2]=>7
100110011=>[1,3,1,3,1,1]=>6
100110100=>[1,3,1,2,3]=>7
100110101=>[1,3,1,2,2,1]=>8
100110110=>[1,3,1,2,1,2]=>7
100110111=>[1,3,1,2,1,1,1]=>6
100111000=>[1,3,1,1,4]=>5
100111001=>[1,3,1,1,3,1]=>6
100111010=>[1,3,1,1,2,2]=>7
100111011=>[1,3,1,1,2,1,1]=>6
100111100=>[1,3,1,1,1,3]=>5
100111101=>[1,3,1,1,1,2,1]=>6
100111110=>[1,3,1,1,1,1,2]=>5
100111111=>[1,3,1,1,1,1,1,1]=>4
101000000=>[1,2,7]=>5
101000001=>[1,2,6,1]=>6
101000010=>[1,2,5,2]=>7
101000011=>[1,2,5,1,1]=>6
101000100=>[1,2,4,3]=>7
101000101=>[1,2,4,2,1]=>8
101000110=>[1,2,4,1,2]=>7
101000111=>[1,2,4,1,1,1]=>6
101001000=>[1,2,3,4]=>7
101001001=>[1,2,3,3,1]=>8
101001010=>[1,2,3,2,2]=>9
101001011=>[1,2,3,2,1,1]=>8
101001100=>[1,2,3,1,3]=>7
101001101=>[1,2,3,1,2,1]=>8
101001110=>[1,2,3,1,1,2]=>7
101001111=>[1,2,3,1,1,1,1]=>6
101010000=>[1,2,2,5]=>7
101010001=>[1,2,2,4,1]=>8
101010010=>[1,2,2,3,2]=>9
101010011=>[1,2,2,3,1,1]=>8
101010100=>[1,2,2,2,3]=>9
101010101=>[1,2,2,2,2,1]=>10
101010110=>[1,2,2,2,1,2]=>9
101010111=>[1,2,2,2,1,1,1]=>8
101011000=>[1,2,2,1,4]=>7
101011001=>[1,2,2,1,3,1]=>8
101011010=>[1,2,2,1,2,2]=>9
101011011=>[1,2,2,1,2,1,1]=>8
101011100=>[1,2,2,1,1,3]=>7
101011101=>[1,2,2,1,1,2,1]=>8
101011110=>[1,2,2,1,1,1,2]=>7
101011111=>[1,2,2,1,1,1,1,1]=>6
101100000=>[1,2,1,6]=>5
101100001=>[1,2,1,5,1]=>6
101100010=>[1,2,1,4,2]=>7
101100011=>[1,2,1,4,1,1]=>6
101100100=>[1,2,1,3,3]=>7
101100101=>[1,2,1,3,2,1]=>8
101100110=>[1,2,1,3,1,2]=>7
101100111=>[1,2,1,3,1,1,1]=>6
101101000=>[1,2,1,2,4]=>7
101101001=>[1,2,1,2,3,1]=>8
101101010=>[1,2,1,2,2,2]=>9
101101011=>[1,2,1,2,2,1,1]=>8
101101100=>[1,2,1,2,1,3]=>7
101101101=>[1,2,1,2,1,2,1]=>8
101101110=>[1,2,1,2,1,1,2]=>7
101101111=>[1,2,1,2,1,1,1,1]=>6
101110000=>[1,2,1,1,5]=>5
101110001=>[1,2,1,1,4,1]=>6
101110010=>[1,2,1,1,3,2]=>7
101110011=>[1,2,1,1,3,1,1]=>6
101110100=>[1,2,1,1,2,3]=>7
101110101=>[1,2,1,1,2,2,1]=>8
101110110=>[1,2,1,1,2,1,2]=>7
101110111=>[1,2,1,1,2,1,1,1]=>6
101111000=>[1,2,1,1,1,4]=>5
101111001=>[1,2,1,1,1,3,1]=>6
101111010=>[1,2,1,1,1,2,2]=>7
101111011=>[1,2,1,1,1,2,1,1]=>6
101111100=>[1,2,1,1,1,1,3]=>5
101111101=>[1,2,1,1,1,1,2,1]=>6
101111110=>[1,2,1,1,1,1,1,2]=>5
101111111=>[1,2,1,1,1,1,1,1,1]=>4
110000000=>[1,1,8]=>3
110000001=>[1,1,7,1]=>4
110000010=>[1,1,6,2]=>5
110000011=>[1,1,6,1,1]=>4
110000100=>[1,1,5,3]=>5
110000101=>[1,1,5,2,1]=>6
110000110=>[1,1,5,1,2]=>5
110000111=>[1,1,5,1,1,1]=>4
110001000=>[1,1,4,4]=>5
110001001=>[1,1,4,3,1]=>6
110001010=>[1,1,4,2,2]=>7
110001011=>[1,1,4,2,1,1]=>6
110001100=>[1,1,4,1,3]=>5
110001101=>[1,1,4,1,2,1]=>6
110001110=>[1,1,4,1,1,2]=>5
110001111=>[1,1,4,1,1,1,1]=>4
110010000=>[1,1,3,5]=>5
110010001=>[1,1,3,4,1]=>6
110010010=>[1,1,3,3,2]=>7
110010011=>[1,1,3,3,1,1]=>6
110010100=>[1,1,3,2,3]=>7
110010101=>[1,1,3,2,2,1]=>8
110010110=>[1,1,3,2,1,2]=>7
110010111=>[1,1,3,2,1,1,1]=>6
110011000=>[1,1,3,1,4]=>5
110011001=>[1,1,3,1,3,1]=>6
110011010=>[1,1,3,1,2,2]=>7
110011011=>[1,1,3,1,2,1,1]=>6
110011100=>[1,1,3,1,1,3]=>5
110011101=>[1,1,3,1,1,2,1]=>6
110011110=>[1,1,3,1,1,1,2]=>5
110011111=>[1,1,3,1,1,1,1,1]=>4
110100000=>[1,1,2,6]=>5
110100001=>[1,1,2,5,1]=>6
110100010=>[1,1,2,4,2]=>7
110100011=>[1,1,2,4,1,1]=>6
110100100=>[1,1,2,3,3]=>7
110100101=>[1,1,2,3,2,1]=>8
110100110=>[1,1,2,3,1,2]=>7
110100111=>[1,1,2,3,1,1,1]=>6
110101000=>[1,1,2,2,4]=>7
110101001=>[1,1,2,2,3,1]=>8
110101010=>[1,1,2,2,2,2]=>9
110101011=>[1,1,2,2,2,1,1]=>8
110101100=>[1,1,2,2,1,3]=>7
110101101=>[1,1,2,2,1,2,1]=>8
110101110=>[1,1,2,2,1,1,2]=>7
110101111=>[1,1,2,2,1,1,1,1]=>6
110110000=>[1,1,2,1,5]=>5
110110001=>[1,1,2,1,4,1]=>6
110110010=>[1,1,2,1,3,2]=>7
110110011=>[1,1,2,1,3,1,1]=>6
110110100=>[1,1,2,1,2,3]=>7
110110101=>[1,1,2,1,2,2,1]=>8
110110110=>[1,1,2,1,2,1,2]=>7
110110111=>[1,1,2,1,2,1,1,1]=>6
110111000=>[1,1,2,1,1,4]=>5
110111001=>[1,1,2,1,1,3,1]=>6
110111010=>[1,1,2,1,1,2,2]=>7
110111011=>[1,1,2,1,1,2,1,1]=>6
110111100=>[1,1,2,1,1,1,3]=>5
110111101=>[1,1,2,1,1,1,2,1]=>6
110111110=>[1,1,2,1,1,1,1,2]=>5
110111111=>[1,1,2,1,1,1,1,1,1]=>4
111000000=>[1,1,1,7]=>3
111000001=>[1,1,1,6,1]=>4
111000010=>[1,1,1,5,2]=>5
111000011=>[1,1,1,5,1,1]=>4
111000100=>[1,1,1,4,3]=>5
111000101=>[1,1,1,4,2,1]=>6
111000110=>[1,1,1,4,1,2]=>5
111000111=>[1,1,1,4,1,1,1]=>4
111001000=>[1,1,1,3,4]=>5
111001001=>[1,1,1,3,3,1]=>6
111001010=>[1,1,1,3,2,2]=>7
111001011=>[1,1,1,3,2,1,1]=>6
111001100=>[1,1,1,3,1,3]=>5
111001101=>[1,1,1,3,1,2,1]=>6
111001110=>[1,1,1,3,1,1,2]=>5
111001111=>[1,1,1,3,1,1,1,1]=>4
111010000=>[1,1,1,2,5]=>5
111010001=>[1,1,1,2,4,1]=>6
111010010=>[1,1,1,2,3,2]=>7
111010011=>[1,1,1,2,3,1,1]=>6
111010100=>[1,1,1,2,2,3]=>7
111010101=>[1,1,1,2,2,2,1]=>8
111010110=>[1,1,1,2,2,1,2]=>7
111010111=>[1,1,1,2,2,1,1,1]=>6
111011000=>[1,1,1,2,1,4]=>5
111011001=>[1,1,1,2,1,3,1]=>6
111011010=>[1,1,1,2,1,2,2]=>7
111011011=>[1,1,1,2,1,2,1,1]=>6
111011100=>[1,1,1,2,1,1,3]=>5
111011101=>[1,1,1,2,1,1,2,1]=>6
111011110=>[1,1,1,2,1,1,1,2]=>5
111011111=>[1,1,1,2,1,1,1,1,1]=>4
111100000=>[1,1,1,1,6]=>3
111100001=>[1,1,1,1,5,1]=>4
111100010=>[1,1,1,1,4,2]=>5
111100011=>[1,1,1,1,4,1,1]=>4
111100100=>[1,1,1,1,3,3]=>5
111100101=>[1,1,1,1,3,2,1]=>6
111100110=>[1,1,1,1,3,1,2]=>5
111100111=>[1,1,1,1,3,1,1,1]=>4
111101000=>[1,1,1,1,2,4]=>5
111101001=>[1,1,1,1,2,3,1]=>6
111101010=>[1,1,1,1,2,2,2]=>7
111101011=>[1,1,1,1,2,2,1,1]=>6
111101100=>[1,1,1,1,2,1,3]=>5
111101101=>[1,1,1,1,2,1,2,1]=>6
111101110=>[1,1,1,1,2,1,1,2]=>5
111101111=>[1,1,1,1,2,1,1,1,1]=>4
111110000=>[1,1,1,1,1,5]=>3
111110001=>[1,1,1,1,1,4,1]=>4
111110010=>[1,1,1,1,1,3,2]=>5
111110011=>[1,1,1,1,1,3,1,1]=>4
111110100=>[1,1,1,1,1,2,3]=>5
111110101=>[1,1,1,1,1,2,2,1]=>6
111110110=>[1,1,1,1,1,2,1,2]=>5
111110111=>[1,1,1,1,1,2,1,1,1]=>4
111111000=>[1,1,1,1,1,1,4]=>3
111111001=>[1,1,1,1,1,1,3,1]=>4
111111010=>[1,1,1,1,1,1,2,2]=>5
111111011=>[1,1,1,1,1,1,2,1,1]=>4
111111100=>[1,1,1,1,1,1,1,3]=>3
111111101=>[1,1,1,1,1,1,1,2,1]=>4
111111110=>[1,1,1,1,1,1,1,1,2]=>3
111111111=>[1,1,1,1,1,1,1,1,1,1]=>2
=>[1]=>1
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Description
The number of corners of the ribbon associated with an integer composition.
We associate a ribbon shape to a composition $c=(c_1,\dots,c_n)$ with $c_i$ cells in the $i$-th row from bottom to top, such that the cells in two rows overlap in precisely one cell.
This statistic records the total number of corners of the ribbon shape.
We associate a ribbon shape to a composition $c=(c_1,\dots,c_n)$ with $c_i$ cells in the $i$-th row from bottom to top, such that the cells in two rows overlap in precisely one cell.
This statistic records the total number of corners of the ribbon shape.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
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