***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St000294 ----------------------------------------------------------------------------- Collection: Binary words ----------------------------------------------------------------------------- Description: The number of distinct factors of a binary word. This is also known as the subword complexity of a binary word, see [1]. ----------------------------------------------------------------------------- References: [1] [[wikipedia:Complexity_function]] ----------------------------------------------------------------------------- Code: def statistic(x): return x.number_of_factors() ----------------------------------------------------------------------------- Statistic values: 0 => 2 1 => 2 00 => 3 01 => 4 10 => 4 11 => 3 000 => 4 001 => 6 010 => 6 011 => 6 100 => 6 101 => 6 110 => 6 111 => 4 0000 => 5 0001 => 8 0010 => 9 0011 => 9 0100 => 9 0101 => 8 0110 => 9 0111 => 8 1000 => 8 1001 => 9 1010 => 8 1011 => 9 1100 => 9 1101 => 9 1110 => 8 1111 => 5 00000 => 6 00001 => 10 00010 => 12 00011 => 12 00100 => 12 00101 => 12 00110 => 13 00111 => 12 01000 => 12 01001 => 12 01010 => 10 01011 => 12 01100 => 13 01101 => 12 01110 => 12 01111 => 10 10000 => 10 10001 => 12 10010 => 12 10011 => 13 10100 => 12 10101 => 10 10110 => 12 10111 => 12 11000 => 12 11001 => 13 11010 => 12 11011 => 12 11100 => 12 11101 => 12 11110 => 10 11111 => 6 000000 => 7 000001 => 12 000010 => 15 000011 => 15 000100 => 16 000101 => 16 000110 => 17 000111 => 16 001000 => 16 001001 => 15 001010 => 15 001011 => 17 001100 => 17 001101 => 17 001110 => 17 001111 => 15 010000 => 15 010001 => 16 010010 => 15 010011 => 17 010100 => 15 010101 => 12 010110 => 16 010111 => 16 011000 => 17 011001 => 17 011010 => 16 011011 => 15 011100 => 17 011101 => 16 011110 => 15 011111 => 12 100000 => 12 100001 => 15 100010 => 16 100011 => 17 100100 => 15 100101 => 16 100110 => 17 100111 => 17 101000 => 16 101001 => 16 101010 => 12 101011 => 15 101100 => 17 101101 => 15 101110 => 16 101111 => 15 110000 => 15 110001 => 17 110010 => 17 110011 => 17 110100 => 17 110101 => 15 110110 => 15 110111 => 16 111000 => 16 111001 => 17 111010 => 16 111011 => 16 111100 => 15 111101 => 15 111110 => 12 111111 => 7 0000000 => 8 0000001 => 14 0000010 => 18 0000011 => 18 0000100 => 20 0000101 => 20 0000110 => 21 0000111 => 20 0001000 => 20 0001001 => 20 0001010 => 20 0001011 => 22 0001100 => 22 0001101 => 22 0001110 => 22 0001111 => 20 0010000 => 20 0010001 => 20 0010010 => 18 0010011 => 21 0010100 => 20 0010101 => 18 0010110 => 22 0010111 => 22 0011000 => 22 0011001 => 21 0011010 => 22 0011011 => 21 0011100 => 22 0011101 => 22 0011110 => 21 0011111 => 18 0100000 => 18 0100001 => 20 0100010 => 20 0100011 => 22 0100100 => 18 0100101 => 20 0100110 => 22 0100111 => 22 0101000 => 20 0101001 => 20 0101010 => 14 0101011 => 18 0101100 => 22 0101101 => 20 0101110 => 21 0101111 => 20 0110000 => 21 0110001 => 22 0110010 => 22 0110011 => 21 0110100 => 22 0110101 => 20 0110110 => 18 0110111 => 20 0111000 => 22 0111001 => 22 0111010 => 21 0111011 => 20 0111100 => 21 0111101 => 20 0111110 => 18 0111111 => 14 1000000 => 14 1000001 => 18 1000010 => 20 1000011 => 21 1000100 => 20 1000101 => 21 1000110 => 22 1000111 => 22 1001000 => 20 1001001 => 18 1001010 => 20 1001011 => 22 1001100 => 21 1001101 => 22 1001110 => 22 1001111 => 21 1010000 => 20 1010001 => 21 1010010 => 20 1010011 => 22 1010100 => 18 1010101 => 14 1010110 => 20 1010111 => 20 1011000 => 22 1011001 => 22 1011010 => 20 1011011 => 18 1011100 => 22 1011101 => 20 1011110 => 20 1011111 => 18 1100000 => 18 1100001 => 21 1100010 => 22 1100011 => 22 1100100 => 21 1100101 => 22 1100110 => 21 1100111 => 22 1101000 => 22 1101001 => 22 1101010 => 18 1101011 => 20 1101100 => 21 1101101 => 18 1101110 => 20 1101111 => 20 1110000 => 20 1110001 => 22 1110010 => 22 1110011 => 22 1110100 => 22 1110101 => 20 1110110 => 20 1110111 => 20 1111000 => 20 1111001 => 21 1111010 => 20 1111011 => 20 1111100 => 18 1111101 => 18 1111110 => 14 1111111 => 8 00000000 => 9 00000001 => 16 00000010 => 21 00000011 => 21 00000100 => 24 00000101 => 24 00000110 => 25 00000111 => 24 00001000 => 25 00001001 => 25 00001010 => 25 00001011 => 27 00001100 => 27 00001101 => 27 00001110 => 27 00001111 => 25 00010000 => 25 00010001 => 24 00010010 => 24 00010011 => 27 00010100 => 26 00010101 => 24 00010110 => 28 00010111 => 28 00011000 => 27 00011001 => 27 00011010 => 28 00011011 => 27 00011100 => 28 00011101 => 28 00011110 => 27 00011111 => 24 00100000 => 24 00100001 => 25 00100010 => 24 00100011 => 27 00100100 => 21 00100101 => 24 00100110 => 27 00100111 => 27 00101000 => 26 00101001 => 25 00101010 => 21 00101011 => 25 00101100 => 28 00101101 => 27 00101110 => 28 00101111 => 27 00110000 => 27 00110001 => 27 00110010 => 27 00110011 => 25 00110100 => 28 00110101 => 27 00110110 => 25 00110111 => 27 00111000 => 28 00111001 => 27 00111010 => 28 00111011 => 27 00111100 => 27 00111101 => 27 00111110 => 25 00111111 => 21 01000000 => 21 01000001 => 24 01000010 => 25 01000011 => 27 01000100 => 24 01000101 => 26 01000110 => 28 01000111 => 28 01001000 => 24 01001001 => 21 01001010 => 25 01001011 => 27 01001100 => 27 01001101 => 28 01001110 => 28 01001111 => 27 01010000 => 25 01010001 => 26 01010010 => 25 01010011 => 27 01010100 => 21 01010101 => 16 01010110 => 24 01010111 => 24 01011000 => 28 01011001 => 28 01011010 => 25 01011011 => 24 01011100 => 28 01011101 => 26 01011110 => 26 01011111 => 24 01100000 => 25 01100001 => 27 01100010 => 28 01100011 => 27 01100100 => 27 01100101 => 28 01100110 => 25 01100111 => 27 01101000 => 28 01101001 => 28 01101010 => 24 01101011 => 25 01101100 => 25 01101101 => 21 01101110 => 25 01101111 => 25 01110000 => 27 01110001 => 28 01110010 => 28 01110011 => 27 01110100 => 28 01110101 => 26 01110110 => 25 01110111 => 24 01111000 => 27 01111001 => 27 01111010 => 26 01111011 => 25 01111100 => 25 01111101 => 24 01111110 => 21 01111111 => 16 10000000 => 16 10000001 => 21 10000010 => 24 10000011 => 25 10000100 => 25 10000101 => 26 10000110 => 27 10000111 => 27 10001000 => 24 10001001 => 25 10001010 => 26 10001011 => 28 10001100 => 27 10001101 => 28 10001110 => 28 10001111 => 27 10010000 => 25 10010001 => 25 10010010 => 21 10010011 => 25 10010100 => 25 10010101 => 24 10010110 => 28 10010111 => 28 10011000 => 27 10011001 => 25 10011010 => 28 10011011 => 27 10011100 => 27 10011101 => 28 10011110 => 27 10011111 => 25 10100000 => 24 10100001 => 26 10100010 => 26 10100011 => 28 10100100 => 24 10100101 => 25 10100110 => 28 10100111 => 28 10101000 => 24 10101001 => 24 10101010 => 16 10101011 => 21 10101100 => 27 10101101 => 25 10101110 => 26 10101111 => 25 10110000 => 27 10110001 => 28 10110010 => 28 10110011 => 27 10110100 => 27 10110101 => 25 10110110 => 21 10110111 => 24 10111000 => 28 10111001 => 28 10111010 => 26 10111011 => 24 10111100 => 27 10111101 => 25 10111110 => 24 10111111 => 21 11000000 => 21 11000001 => 25 11000010 => 27 11000011 => 27 11000100 => 27 11000101 => 28 11000110 => 27 11000111 => 28 11001000 => 27 11001001 => 25 11001010 => 27 11001011 => 28 11001100 => 25 11001101 => 27 11001110 => 27 11001111 => 27 11010000 => 27 11010001 => 28 11010010 => 27 11010011 => 28 11010100 => 25 11010101 => 21 11010110 => 25 11010111 => 26 11011000 => 27 11011001 => 27 11011010 => 24 11011011 => 21 11011100 => 27 11011101 => 24 11011110 => 25 11011111 => 24 11100000 => 24 11100001 => 27 11100010 => 28 11100011 => 28 11100100 => 27 11100101 => 28 11100110 => 27 11100111 => 27 11101000 => 28 11101001 => 28 11101010 => 24 11101011 => 26 11101100 => 27 11101101 => 24 11101110 => 24 11101111 => 25 11110000 => 25 11110001 => 27 11110010 => 27 11110011 => 27 11110100 => 27 11110101 => 25 11110110 => 25 11110111 => 25 11111000 => 24 11111001 => 25 11111010 => 24 11111011 => 24 11111100 => 21 11111101 => 21 11111110 => 16 11111111 => 9 000000000 => 10 000000001 => 18 000000010 => 24 000000011 => 24 000000100 => 28 000000101 => 28 000000110 => 29 000000111 => 28 000001000 => 30 000001001 => 30 000001010 => 30 000001011 => 32 000001100 => 32 000001101 => 32 000001110 => 32 000001111 => 30 000010000 => 30 000010001 => 30 000010010 => 30 000010011 => 33 000010100 => 32 000010101 => 30 000010110 => 34 000010111 => 34 000011000 => 33 000011001 => 33 000011010 => 34 000011011 => 33 000011100 => 34 000011101 => 34 000011110 => 33 000011111 => 30 000100000 => 30 000100001 => 30 000100010 => 28 000100011 => 32 000100100 => 28 000100101 => 31 000100110 => 34 000100111 => 34 000101000 => 32 000101001 => 32 000101010 => 28 000101011 => 32 000101100 => 35 000101101 => 34 000101110 => 35 000101111 => 34 000110000 => 33 000110001 => 32 000110010 => 34 000110011 => 32 000110100 => 35 000110101 => 34 000110110 => 32 000110111 => 34 000111000 => 34 000111001 => 34 000111010 => 35 000111011 => 34 000111100 => 34 000111101 => 34 000111110 => 32 000111111 => 28 001000000 => 28 001000001 => 30 001000010 => 30 001000011 => 33 001000100 => 28 001000101 => 31 001000110 => 34 001000111 => 34 001001000 => 28 001001001 => 24 001001010 => 30 001001011 => 32 001001100 => 33 001001101 => 34 001001110 => 34 001001111 => 33 001010000 => 32 001010001 => 32 001010010 => 30 001010011 => 33 001010100 => 28 001010101 => 24 001010110 => 32 001010111 => 32 001011000 => 35 001011001 => 34 001011010 => 33 001011011 => 32 001011100 => 35 001011101 => 34 001011110 => 34 001011111 => 32 001100000 => 32 001100001 => 33 001100010 => 34 001100011 => 32 001100100 => 33 001100101 => 34 001100110 => 29 001100111 => 32 001101000 => 35 001101001 => 34 001101010 => 32 001101011 => 33 001101100 => 32 001101101 => 29 001101110 => 33 001101111 => 33 001110000 => 34 001110001 => 34 001110010 => 34 001110011 => 32 001110100 => 35 001110101 => 34 001110110 => 33 001110111 => 32 001111000 => 34 001111001 => 33 001111010 => 34 001111011 => 33 001111100 => 32 001111101 => 32 001111110 => 29 001111111 => 24 010000000 => 24 010000001 => 28 010000010 => 30 010000011 => 32 010000100 => 30 010000101 => 32 010000110 => 34 010000111 => 34 010001000 => 28 010001001 => 30 010001010 => 32 010001011 => 34 010001100 => 34 010001101 => 35 010001110 => 35 010001111 => 34 010010000 => 30 010010001 => 30 010010010 => 24 010010011 => 29 010010100 => 30 010010101 => 30 010010110 => 34 010010111 => 34 010011000 => 34 010011001 => 32 010011010 => 34 010011011 => 34 010011100 => 34 010011101 => 35 010011110 => 34 010011111 => 32 010100000 => 30 010100001 => 32 010100010 => 32 010100011 => 34 010100100 => 30 010100101 => 30 010100110 => 34 010100111 => 34 010101000 => 28 010101001 => 28 010101010 => 18 010101011 => 24 010101100 => 32 010101101 => 30 010101110 => 31 010101111 => 30 010110000 => 34 010110001 => 35 010110010 => 34 010110011 => 34 010110100 => 33 010110101 => 30 010110110 => 28 010110111 => 31 010111000 => 35 010111001 => 35 010111010 => 32 010111011 => 31 010111100 => 34 010111101 => 32 010111110 => 31 010111111 => 28 011000000 => 29 011000001 => 32 011000010 => 34 011000011 => 33 011000100 => 34 011000101 => 35 011000110 => 32 011000111 => 34 011001000 => 34 011001001 => 32 011001010 => 34 011001011 => 34 011001100 => 29 011001101 => 32 011001110 => 33 011001111 => 33 011010000 => 34 011010001 => 35 011010010 => 34 011010011 => 34 011010100 => 32 011010101 => 28 011010110 => 30 011010111 => 32 011011000 => 32 011011001 => 32 011011010 => 28 011011011 => 24 011011100 => 33 011011101 => 30 011011110 => 31 011011111 => 30 011100000 => 32 011100001 => 34 011100010 => 35 011100011 => 34 011100100 => 34 011100101 => 35 011100110 => 33 011100111 => 32 011101000 => 35 011101001 => 35 011101010 => 31 011101011 => 32 011101100 => 33 011101101 => 30 011101110 => 28 011101111 => 30 011110000 => 33 011110001 => 34 011110010 => 34 011110011 => 33 011110100 => 34 011110101 => 32 011110110 => 31 011110111 => 30 011111000 => 32 011111001 => 32 011111010 => 31 011111011 => 30 011111100 => 29 011111101 => 28 011111110 => 24 011111111 => 18 100000000 => 18 100000001 => 24 100000010 => 28 100000011 => 29 100000100 => 30 100000101 => 31 100000110 => 32 100000111 => 32 100001000 => 30 100001001 => 31 100001010 => 32 100001011 => 34 100001100 => 33 100001101 => 34 100001110 => 34 100001111 => 33 100010000 => 30 100010001 => 28 100010010 => 30 100010011 => 33 100010100 => 32 100010101 => 31 100010110 => 35 100010111 => 35 100011000 => 32 100011001 => 33 100011010 => 35 100011011 => 34 100011100 => 34 100011101 => 35 100011110 => 34 100011111 => 32 100100000 => 30 100100001 => 31 100100010 => 30 100100011 => 33 100100100 => 24 100100101 => 28 100100110 => 32 100100111 => 32 100101000 => 32 100101001 => 30 100101010 => 28 100101011 => 32 100101100 => 34 100101101 => 34 100101110 => 35 100101111 => 34 100110000 => 33 100110001 => 33 100110010 => 32 100110011 => 29 100110100 => 34 100110101 => 34 100110110 => 32 100110111 => 34 100111000 => 34 100111001 => 32 100111010 => 35 100111011 => 34 100111100 => 33 100111101 => 34 100111110 => 32 100111111 => 29 101000000 => 28 101000001 => 31 101000010 => 32 101000011 => 34 101000100 => 31 101000101 => 32 101000110 => 35 101000111 => 35 101001000 => 31 101001001 => 28 101001010 => 30 101001011 => 33 101001100 => 34 101001101 => 34 101001110 => 35 101001111 => 34 101010000 => 30 101010001 => 31 101010010 => 30 101010011 => 32 101010100 => 24 101010101 => 18 101010110 => 28 101010111 => 28 101011000 => 34 101011001 => 34 101011010 => 30 101011011 => 30 101011100 => 34 101011101 => 32 101011110 => 32 101011111 => 30 101100000 => 32 101100001 => 34 101100010 => 35 101100011 => 34 101100100 => 34 101100101 => 34 101100110 => 32 101100111 => 34 101101000 => 34 101101001 => 34 101101010 => 30 101101011 => 30 101101100 => 29 101101101 => 24 101101110 => 30 101101111 => 30 101110000 => 34 101110001 => 35 101110010 => 35 101110011 => 34 101110100 => 34 101110101 => 32 101110110 => 30 101110111 => 28 101111000 => 34 101111001 => 34 101111010 => 32 101111011 => 30 101111100 => 32 101111101 => 30 101111110 => 28 101111111 => 24 110000000 => 24 110000001 => 29 110000010 => 32 110000011 => 32 110000100 => 33 110000101 => 34 110000110 => 33 110000111 => 34 110001000 => 32 110001001 => 33 110001010 => 34 110001011 => 35 110001100 => 32 110001101 => 34 110001110 => 34 110001111 => 34 110010000 => 33 110010001 => 33 110010010 => 29 110010011 => 32 110010100 => 33 110010101 => 32 110010110 => 34 110010111 => 35 110011000 => 32 110011001 => 29 110011010 => 34 110011011 => 33 110011100 => 32 110011101 => 34 110011110 => 33 110011111 => 32 110100000 => 32 110100001 => 34 110100010 => 34 110100011 => 35 110100100 => 32 110100101 => 33 110100110 => 34 110100111 => 35 110101000 => 32 110101001 => 32 110101010 => 24 110101011 => 28 110101100 => 33 110101101 => 30 110101110 => 32 110101111 => 32 110110000 => 33 110110001 => 34 110110010 => 34 110110011 => 33 110110100 => 32 110110101 => 30 110110110 => 24 110110111 => 28 110111000 => 34 110111001 => 34 110111010 => 31 110111011 => 28 110111100 => 33 110111101 => 30 110111110 => 30 110111111 => 28 111000000 => 28 111000001 => 32 111000010 => 34 111000011 => 34 111000100 => 34 111000101 => 35 111000110 => 34 111000111 => 34 111001000 => 34 111001001 => 32 111001010 => 34 111001011 => 35 111001100 => 32 111001101 => 34 111001110 => 32 111001111 => 33 111010000 => 34 111010001 => 35 111010010 => 34 111010011 => 35 111010100 => 32 111010101 => 28 111010110 => 32 111010111 => 32 111011000 => 34 111011001 => 34 111011010 => 31 111011011 => 28 111011100 => 32 111011101 => 28 111011110 => 30 111011111 => 30 111100000 => 30 111100001 => 33 111100010 => 34 111100011 => 34 111100100 => 33 111100101 => 34 111100110 => 33 111100111 => 33 111101000 => 34 111101001 => 34 111101010 => 30 111101011 => 32 111101100 => 33 111101101 => 30 111101110 => 30 111101111 => 30 111110000 => 30 111110001 => 32 111110010 => 32 111110011 => 32 111110100 => 32 111110101 => 30 111110110 => 30 111110111 => 30 111111000 => 28 111111001 => 29 111111010 => 28 111111011 => 28 111111100 => 24 111111101 => 24 111111110 => 18 111111111 => 10 0000000001 => 20 0010000001 => 35 0010101101 => 39 0010101011 => 33 0010100111 => 41 0010011101 => 42 0010011011 => 41 0010010111 => 40 0010001111 => 41 0001110101 => 42 0001110011 => 40 0001101101 => 37 0001101011 => 41 0001100111 => 40 0001011101 => 42 0001011011 => 40 0001010111 => 40 0001001111 => 41 0000111101 => 41 0000111011 => 41 0000110111 => 41 0000101111 => 41 0000011111 => 36 0000000000 => 11 0000000110 => 33 0000011000 => 39 0000011110 => 39 0000010010 => 36 0001100000 => 39 0001100110 => 37 0001111000 => 41 0001111110 => 37 0001110010 => 42 0001001000 => 35 0001001110 => 42 0001000010 => 35 0001011010 => 41 0010101010 => 27 0010101000 => 36 0010101100 => 40 0010100100 => 36 0010010100 => 36 0001010100 => 36 0010101110 => 40 0010100000 => 38 0010000100 => 35 0000010100 => 38 0000000010 => 27 0000001110 => 37 0000111110 => 39 0000000100 => 32 0000001010 => 35 0000010110 => 40 0000101110 => 42 0001011110 => 42 0001101110 => 41 0001110110 => 41 0001111010 => 42 0001111100 => 40 0000000101 => 32 0000001101 => 37 0000011101 => 40 0001111101 => 40 0000001001 => 35 0000010101 => 36 0000101101 => 41 0010110001 => 42 0001100001 => 39 0001000001 => 36 0000111111 => 35 0001110100 => 43 0001101100 => 40 0010011100 => 41 0001011100 => 43 0000111100 => 41 0001101010 => 40 0010011010 => 41 0000111010 => 42 0010100110 => 41 0010010110 => 40 0001010110 => 40 0000110110 => 39 0010001110 => 42 0001101001 => 42 0000110001 => 39 0000010001 => 36 0000001100 => 37 0000011001 => 39 0000110011 => 39 0000110100 => 42 0000000011 => 27 0000011011 => 39 0001101111 => 41 0000110101 => 41 0010000010 => 36 0001000011 => 39 0010011110 => 41 0001010000 => 39 0001000100 => 32 0001010101 => 32 0001001011 => 40 0001100011 => 37 0001110111 => 40 0010000000 => 32 0000000111 => 32 0000001111 => 35 0001111111 => 32 0000001011 => 37 0000010111 => 40 0001011111 => 40 0001111001 => 41 0000011010 => 40 0000101010 => 35 0000100101 => 38 0010010001 => 35 0010000101 => 38 0010010101 => 36 0010010011 => 33 0000101011 => 39 0001000111 => 40 0000100111 => 41 0010010010 => 27 0001001010 => 38 0001001001 => 32 0001000101 => 36 0000100011 => 39 0000100100 => 35 0000100010 => 35 0010110000 => 42 0000011100 => 40 0000001000 => 35 0000101100 => 42 0010101111 => 39 0000101000 => 39 0010001000 => 32 0001001100 => 41 0001000110 => 40 0001100100 => 41 0001100010 => 40 0000100110 => 41 0000110010 => 41 0010010000 => 35 0001010010 => 38 0001000000 => 35 0001011001 => 42 0001100101 => 42 0001110001 => 40 0010011001 => 39 0010100101 => 35 0010101001 => 35 0010011111 => 39 0000111001 => 41 0010001101 => 42 0001001101 => 42 0001010001 => 38 0001010011 => 41 0001111011 => 41 0010011000 => 41 0001011000 => 42 0000100000 => 36 0010001011 => 40 0010000111 => 41 0000010011 => 39 0010001100 => 41 0010000110 => 41 0000110000 => 39 0000100001 => 35 0010100011 => 41 0010100001 => 39 0000111000 => 41 0001101000 => 42 0000010000 => 36 0000101001 => 39 0010100010 => 38 0010001001 => 35 0010000011 => 39 0010001010 => 38 0001110000 => 41 ----------------------------------------------------------------------------- Created: Nov 19, 2015 at 12:16 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jun 03, 2016 at 11:21 by Martin Rubey