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* www.FindStat.org - The Combinatorial Statistic Finder *
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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* 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. *
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-----------------------------------------------------------------------------
Statistic identifier: St000691
-----------------------------------------------------------------------------
Collection: Binary words
-----------------------------------------------------------------------------
Description: The number of changes of a binary word.
This is the number of indices $i$ such that $w_i \neq w_{i+1}$.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(w):
return sum( 1 for i in range(len(w)-Integer(1)) if w[i] != w[i+1] )
-----------------------------------------------------------------------------
Statistic values:
0 => 0
1 => 0
00 => 0
01 => 1
10 => 1
11 => 0
000 => 0
001 => 1
010 => 2
011 => 1
100 => 1
101 => 2
110 => 1
111 => 0
0000 => 0
0001 => 1
0010 => 2
0011 => 1
0100 => 2
0101 => 3
0110 => 2
0111 => 1
1000 => 1
1001 => 2
1010 => 3
1011 => 2
1100 => 1
1101 => 2
1110 => 1
1111 => 0
00000 => 0
00001 => 1
00010 => 2
00011 => 1
00100 => 2
00101 => 3
00110 => 2
00111 => 1
01000 => 2
01001 => 3
01010 => 4
01011 => 3
01100 => 2
01101 => 3
01110 => 2
01111 => 1
10000 => 1
10001 => 2
10010 => 3
10011 => 2
10100 => 3
10101 => 4
10110 => 3
10111 => 2
11000 => 1
11001 => 2
11010 => 3
11011 => 2
11100 => 1
11101 => 2
11110 => 1
11111 => 0
000000 => 0
000001 => 1
000010 => 2
000011 => 1
000100 => 2
000101 => 3
000110 => 2
000111 => 1
001000 => 2
001001 => 3
001010 => 4
001011 => 3
001100 => 2
001101 => 3
001110 => 2
001111 => 1
010000 => 2
010001 => 3
010010 => 4
010011 => 3
010100 => 4
010101 => 5
010110 => 4
010111 => 3
011000 => 2
011001 => 3
011010 => 4
011011 => 3
011100 => 2
011101 => 3
011110 => 2
011111 => 1
100000 => 1
100001 => 2
100010 => 3
100011 => 2
100100 => 3
100101 => 4
100110 => 3
100111 => 2
101000 => 3
101001 => 4
101010 => 5
101011 => 4
101100 => 3
101101 => 4
101110 => 3
101111 => 2
110000 => 1
110001 => 2
110010 => 3
110011 => 2
110100 => 3
110101 => 4
110110 => 3
110111 => 2
111000 => 1
111001 => 2
111010 => 3
111011 => 2
111100 => 1
111101 => 2
111110 => 1
111111 => 0
0000000 => 0
0000001 => 1
0000010 => 2
0000011 => 1
0000100 => 2
0000101 => 3
0000110 => 2
0000111 => 1
0001000 => 2
0001001 => 3
0001010 => 4
0001011 => 3
0001100 => 2
0001101 => 3
0001110 => 2
0001111 => 1
0010000 => 2
0010001 => 3
0010010 => 4
0010011 => 3
0010100 => 4
0010101 => 5
0010110 => 4
0010111 => 3
0011000 => 2
0011001 => 3
0011010 => 4
0011011 => 3
0011100 => 2
0011101 => 3
0011110 => 2
0011111 => 1
0100000 => 2
0100001 => 3
0100010 => 4
0100011 => 3
0100100 => 4
0100101 => 5
0100110 => 4
0100111 => 3
0101000 => 4
0101001 => 5
0101010 => 6
0101011 => 5
0101100 => 4
0101101 => 5
0101110 => 4
0101111 => 3
0110000 => 2
0110001 => 3
0110010 => 4
0110011 => 3
0110100 => 4
0110101 => 5
0110110 => 4
0110111 => 3
0111000 => 2
0111001 => 3
0111010 => 4
0111011 => 3
0111100 => 2
0111101 => 3
0111110 => 2
0111111 => 1
1000000 => 1
1000001 => 2
1000010 => 3
1000011 => 2
1000100 => 3
1000101 => 4
1000110 => 3
1000111 => 2
1001000 => 3
1001001 => 4
1001010 => 5
1001011 => 4
1001100 => 3
1001101 => 4
1001110 => 3
1001111 => 2
1010000 => 3
1010001 => 4
1010010 => 5
1010011 => 4
1010100 => 5
1010101 => 6
1010110 => 5
1010111 => 4
1011000 => 3
1011001 => 4
1011010 => 5
1011011 => 4
1011100 => 3
1011101 => 4
1011110 => 3
1011111 => 2
1100000 => 1
1100001 => 2
1100010 => 3
1100011 => 2
1100100 => 3
1100101 => 4
1100110 => 3
1100111 => 2
1101000 => 3
1101001 => 4
1101010 => 5
1101011 => 4
1101100 => 3
1101101 => 4
1101110 => 3
1101111 => 2
1110000 => 1
1110001 => 2
1110010 => 3
1110011 => 2
1110100 => 3
1110101 => 4
1110110 => 3
1110111 => 2
1111000 => 1
1111001 => 2
1111010 => 3
1111011 => 2
1111100 => 1
1111101 => 2
1111110 => 1
1111111 => 0
00000000 => 0
00000001 => 1
00000010 => 2
00000011 => 1
00000100 => 2
00000101 => 3
00000110 => 2
00000111 => 1
00001000 => 2
00001001 => 3
00001010 => 4
00001011 => 3
00001100 => 2
00001101 => 3
00001110 => 2
00001111 => 1
00010000 => 2
00010001 => 3
00010010 => 4
00010011 => 3
00010100 => 4
00010101 => 5
00010110 => 4
00010111 => 3
00011000 => 2
00011001 => 3
00011010 => 4
00011011 => 3
00011100 => 2
00011101 => 3
00011110 => 2
00011111 => 1
00100000 => 2
00100001 => 3
00100010 => 4
00100011 => 3
00100100 => 4
00100101 => 5
00100110 => 4
00100111 => 3
00101000 => 4
00101001 => 5
00101010 => 6
00101011 => 5
00101100 => 4
00101101 => 5
00101110 => 4
00101111 => 3
00110000 => 2
00110001 => 3
00110010 => 4
00110011 => 3
00110100 => 4
00110101 => 5
00110110 => 4
00110111 => 3
00111000 => 2
00111001 => 3
00111010 => 4
00111011 => 3
00111100 => 2
00111101 => 3
00111110 => 2
00111111 => 1
01000000 => 2
01000001 => 3
01000010 => 4
01000011 => 3
01000100 => 4
01000101 => 5
01000110 => 4
01000111 => 3
01001000 => 4
01001001 => 5
01001010 => 6
01001011 => 5
01001100 => 4
01001101 => 5
01001110 => 4
01001111 => 3
01010000 => 4
01010001 => 5
01010010 => 6
01010011 => 5
01010100 => 6
01010101 => 7
01010110 => 6
01010111 => 5
01011000 => 4
01011001 => 5
01011010 => 6
01011011 => 5
01011100 => 4
01011101 => 5
01011110 => 4
01011111 => 3
01100000 => 2
01100001 => 3
01100010 => 4
01100011 => 3
01100100 => 4
01100101 => 5
01100110 => 4
01100111 => 3
01101000 => 4
01101001 => 5
01101010 => 6
01101011 => 5
01101100 => 4
01101101 => 5
01101110 => 4
01101111 => 3
01110000 => 2
01110001 => 3
01110010 => 4
01110011 => 3
01110100 => 4
01110101 => 5
01110110 => 4
01110111 => 3
01111000 => 2
01111001 => 3
01111010 => 4
01111011 => 3
01111100 => 2
01111101 => 3
01111110 => 2
01111111 => 1
10000000 => 1
10000001 => 2
10000010 => 3
10000011 => 2
10000100 => 3
10000101 => 4
10000110 => 3
10000111 => 2
10001000 => 3
10001001 => 4
10001010 => 5
10001011 => 4
10001100 => 3
10001101 => 4
10001110 => 3
10001111 => 2
10010000 => 3
10010001 => 4
10010010 => 5
10010011 => 4
10010100 => 5
10010101 => 6
10010110 => 5
10010111 => 4
10011000 => 3
10011001 => 4
10011010 => 5
10011011 => 4
10011100 => 3
10011101 => 4
10011110 => 3
10011111 => 2
10100000 => 3
10100001 => 4
10100010 => 5
10100011 => 4
10100100 => 5
10100101 => 6
10100110 => 5
10100111 => 4
10101000 => 5
10101001 => 6
10101010 => 7
10101011 => 6
10101100 => 5
10101101 => 6
10101110 => 5
10101111 => 4
10110000 => 3
10110001 => 4
10110010 => 5
10110011 => 4
10110100 => 5
10110101 => 6
10110110 => 5
10110111 => 4
10111000 => 3
10111001 => 4
10111010 => 5
10111011 => 4
10111100 => 3
10111101 => 4
10111110 => 3
10111111 => 2
11000000 => 1
11000001 => 2
11000010 => 3
11000011 => 2
11000100 => 3
11000101 => 4
11000110 => 3
11000111 => 2
11001000 => 3
11001001 => 4
11001010 => 5
11001011 => 4
11001100 => 3
11001101 => 4
11001110 => 3
11001111 => 2
11010000 => 3
11010001 => 4
11010010 => 5
11010011 => 4
11010100 => 5
11010101 => 6
11010110 => 5
11010111 => 4
11011000 => 3
11011001 => 4
11011010 => 5
11011011 => 4
11011100 => 3
11011101 => 4
11011110 => 3
11011111 => 2
11100000 => 1
11100001 => 2
11100010 => 3
11100011 => 2
11100100 => 3
11100101 => 4
11100110 => 3
11100111 => 2
11101000 => 3
11101001 => 4
11101010 => 5
11101011 => 4
11101100 => 3
11101101 => 4
11101110 => 3
11101111 => 2
11110000 => 1
11110001 => 2
11110010 => 3
11110011 => 2
11110100 => 3
11110101 => 4
11110110 => 3
11110111 => 2
11111000 => 1
11111001 => 2
11111010 => 3
11111011 => 2
11111100 => 1
11111101 => 2
11111110 => 1
11111111 => 0
000000000 => 0
000000001 => 1
000000010 => 2
000000011 => 1
000000100 => 2
000000101 => 3
000000110 => 2
000000111 => 1
000001000 => 2
000001001 => 3
000001010 => 4
000001011 => 3
000001100 => 2
000001101 => 3
000001110 => 2
000001111 => 1
000010000 => 2
000010001 => 3
000010010 => 4
000010011 => 3
000010100 => 4
000010101 => 5
000010110 => 4
000010111 => 3
000011000 => 2
000011001 => 3
000011010 => 4
000011011 => 3
000011100 => 2
000011101 => 3
000011110 => 2
000011111 => 1
000100000 => 2
000100001 => 3
000100010 => 4
000100011 => 3
000100100 => 4
000100101 => 5
000100110 => 4
000100111 => 3
000101000 => 4
000101001 => 5
000101010 => 6
000101011 => 5
000101100 => 4
000101101 => 5
000101110 => 4
000101111 => 3
000110000 => 2
000110001 => 3
000110010 => 4
000110011 => 3
000110100 => 4
000110101 => 5
000110110 => 4
000110111 => 3
000111000 => 2
000111001 => 3
000111010 => 4
000111011 => 3
000111100 => 2
000111101 => 3
000111110 => 2
000111111 => 1
001000000 => 2
001000001 => 3
001000010 => 4
001000011 => 3
001000100 => 4
001000101 => 5
001000110 => 4
001000111 => 3
001001000 => 4
001001001 => 5
001001010 => 6
001001011 => 5
001001100 => 4
001001101 => 5
001001110 => 4
001001111 => 3
001010000 => 4
001010001 => 5
001010010 => 6
001010011 => 5
001010100 => 6
001010101 => 7
001010110 => 6
001010111 => 5
001011000 => 4
001011001 => 5
001011010 => 6
001011011 => 5
001011100 => 4
001011101 => 5
001011110 => 4
001011111 => 3
001100000 => 2
001100001 => 3
001100010 => 4
001100011 => 3
001100100 => 4
001100101 => 5
001100110 => 4
001100111 => 3
001101000 => 4
001101001 => 5
001101010 => 6
001101011 => 5
001101100 => 4
001101101 => 5
001101110 => 4
001101111 => 3
001110000 => 2
001110001 => 3
001110010 => 4
001110011 => 3
001110100 => 4
001110101 => 5
001110110 => 4
001110111 => 3
001111000 => 2
001111001 => 3
001111010 => 4
001111011 => 3
001111100 => 2
001111101 => 3
001111110 => 2
001111111 => 1
010000000 => 2
010000001 => 3
010000010 => 4
010000011 => 3
010000100 => 4
010000101 => 5
010000110 => 4
010000111 => 3
010001000 => 4
010001001 => 5
010001010 => 6
010001011 => 5
010001100 => 4
010001101 => 5
010001110 => 4
010001111 => 3
010010000 => 4
010010001 => 5
010010010 => 6
010010011 => 5
010010100 => 6
010010101 => 7
010010110 => 6
010010111 => 5
010011000 => 4
010011001 => 5
010011010 => 6
010011011 => 5
010011100 => 4
010011101 => 5
010011110 => 4
010011111 => 3
010100000 => 4
010100001 => 5
010100010 => 6
010100011 => 5
010100100 => 6
010100101 => 7
010100110 => 6
010100111 => 5
010101000 => 6
010101001 => 7
010101010 => 8
010101011 => 7
010101100 => 6
010101101 => 7
010101110 => 6
010101111 => 5
010110000 => 4
010110001 => 5
010110010 => 6
010110011 => 5
010110100 => 6
010110101 => 7
010110110 => 6
010110111 => 5
010111000 => 4
010111001 => 5
010111010 => 6
010111011 => 5
010111100 => 4
010111101 => 5
010111110 => 4
010111111 => 3
011000000 => 2
011000001 => 3
011000010 => 4
011000011 => 3
011000100 => 4
011000101 => 5
011000110 => 4
011000111 => 3
011001000 => 4
011001001 => 5
011001010 => 6
011001011 => 5
011001100 => 4
011001101 => 5
011001110 => 4
011001111 => 3
011010000 => 4
011010001 => 5
011010010 => 6
011010011 => 5
011010100 => 6
011010101 => 7
011010110 => 6
011010111 => 5
011011000 => 4
011011001 => 5
011011010 => 6
011011011 => 5
011011100 => 4
011011101 => 5
011011110 => 4
011011111 => 3
011100000 => 2
011100001 => 3
011100010 => 4
011100011 => 3
011100100 => 4
011100101 => 5
011100110 => 4
011100111 => 3
011101000 => 4
011101001 => 5
011101010 => 6
011101011 => 5
011101100 => 4
011101101 => 5
011101110 => 4
011101111 => 3
011110000 => 2
011110001 => 3
011110010 => 4
011110011 => 3
011110100 => 4
011110101 => 5
011110110 => 4
011110111 => 3
011111000 => 2
011111001 => 3
011111010 => 4
011111011 => 3
011111100 => 2
011111101 => 3
011111110 => 2
011111111 => 1
100000000 => 1
100000001 => 2
100000010 => 3
100000011 => 2
100000100 => 3
100000101 => 4
100000110 => 3
100000111 => 2
100001000 => 3
100001001 => 4
100001010 => 5
100001011 => 4
100001100 => 3
100001101 => 4
100001110 => 3
100001111 => 2
100010000 => 3
100010001 => 4
100010010 => 5
100010011 => 4
100010100 => 5
100010101 => 6
100010110 => 5
100010111 => 4
100011000 => 3
100011001 => 4
100011010 => 5
100011011 => 4
100011100 => 3
100011101 => 4
100011110 => 3
100011111 => 2
100100000 => 3
100100001 => 4
100100010 => 5
100100011 => 4
100100100 => 5
100100101 => 6
100100110 => 5
100100111 => 4
100101000 => 5
100101001 => 6
100101010 => 7
100101011 => 6
100101100 => 5
100101101 => 6
100101110 => 5
100101111 => 4
100110000 => 3
100110001 => 4
100110010 => 5
100110011 => 4
100110100 => 5
100110101 => 6
100110110 => 5
100110111 => 4
100111000 => 3
100111001 => 4
100111010 => 5
100111011 => 4
100111100 => 3
100111101 => 4
100111110 => 3
100111111 => 2
101000000 => 3
101000001 => 4
101000010 => 5
101000011 => 4
101000100 => 5
101000101 => 6
101000110 => 5
101000111 => 4
101001000 => 5
101001001 => 6
101001010 => 7
101001011 => 6
101001100 => 5
101001101 => 6
101001110 => 5
101001111 => 4
101010000 => 5
101010001 => 6
101010010 => 7
101010011 => 6
101010100 => 7
101010101 => 8
101010110 => 7
101010111 => 6
101011000 => 5
101011001 => 6
101011010 => 7
101011011 => 6
101011100 => 5
101011101 => 6
101011110 => 5
101011111 => 4
101100000 => 3
101100001 => 4
101100010 => 5
101100011 => 4
101100100 => 5
101100101 => 6
101100110 => 5
101100111 => 4
101101000 => 5
101101001 => 6
101101010 => 7
101101011 => 6
101101100 => 5
101101101 => 6
101101110 => 5
101101111 => 4
101110000 => 3
101110001 => 4
101110010 => 5
101110011 => 4
101110100 => 5
101110101 => 6
101110110 => 5
101110111 => 4
101111000 => 3
101111001 => 4
101111010 => 5
101111011 => 4
101111100 => 3
101111101 => 4
101111110 => 3
101111111 => 2
110000000 => 1
110000001 => 2
110000010 => 3
110000011 => 2
110000100 => 3
110000101 => 4
110000110 => 3
110000111 => 2
110001000 => 3
110001001 => 4
110001010 => 5
110001011 => 4
110001100 => 3
110001101 => 4
110001110 => 3
110001111 => 2
110010000 => 3
110010001 => 4
110010010 => 5
110010011 => 4
110010100 => 5
110010101 => 6
110010110 => 5
110010111 => 4
110011000 => 3
110011001 => 4
110011010 => 5
110011011 => 4
110011100 => 3
110011101 => 4
110011110 => 3
110011111 => 2
110100000 => 3
110100001 => 4
110100010 => 5
110100011 => 4
110100100 => 5
110100101 => 6
110100110 => 5
110100111 => 4
110101000 => 5
110101001 => 6
110101010 => 7
110101011 => 6
110101100 => 5
110101101 => 6
110101110 => 5
110101111 => 4
110110000 => 3
110110001 => 4
110110010 => 5
110110011 => 4
110110100 => 5
110110101 => 6
110110110 => 5
110110111 => 4
110111000 => 3
110111001 => 4
110111010 => 5
110111011 => 4
110111100 => 3
110111101 => 4
110111110 => 3
110111111 => 2
111000000 => 1
111000001 => 2
111000010 => 3
111000011 => 2
111000100 => 3
111000101 => 4
111000110 => 3
111000111 => 2
111001000 => 3
111001001 => 4
111001010 => 5
111001011 => 4
111001100 => 3
111001101 => 4
111001110 => 3
111001111 => 2
111010000 => 3
111010001 => 4
111010010 => 5
111010011 => 4
111010100 => 5
111010101 => 6
111010110 => 5
111010111 => 4
111011000 => 3
111011001 => 4
111011010 => 5
111011011 => 4
111011100 => 3
111011101 => 4
111011110 => 3
111011111 => 2
111100000 => 1
111100001 => 2
111100010 => 3
111100011 => 2
111100100 => 3
111100101 => 4
111100110 => 3
111100111 => 2
111101000 => 3
111101001 => 4
111101010 => 5
111101011 => 4
111101100 => 3
111101101 => 4
111101110 => 3
111101111 => 2
111110000 => 1
111110001 => 2
111110010 => 3
111110011 => 2
111110100 => 3
111110101 => 4
111110110 => 3
111110111 => 2
111111000 => 1
111111001 => 2
111111010 => 3
111111011 => 2
111111100 => 1
111111101 => 2
111111110 => 1
111111111 => 0
0000000001 => 1
0010000001 => 3
0010101101 => 7
0010101011 => 7
0010100111 => 5
0010011101 => 5
0010011011 => 5
0010010111 => 5
0010001111 => 3
0001110101 => 5
0001110011 => 3
0001101101 => 5
0001101011 => 5
0001100111 => 3
0001011101 => 5
0001011011 => 5
0001010111 => 5
0001001111 => 3
0000111101 => 3
0000111011 => 3
0000110111 => 3
0000101111 => 3
0000011111 => 1
0000000000 => 0
0000000110 => 2
0000011000 => 2
0000011110 => 2
0000010010 => 4
0001100000 => 2
0001100110 => 4
0001111000 => 2
0001111110 => 2
0001110010 => 4
0001001000 => 4
0001001110 => 4
0001000010 => 4
0001011010 => 6
0010101010 => 8
0010101000 => 6
0010101100 => 6
0010100100 => 6
0010010100 => 6
0001010100 => 6
0010101110 => 6
0010100000 => 4
0010000100 => 4
0000010100 => 4
0000000010 => 2
0000001110 => 2
0000111110 => 2
0000000100 => 2
0000001010 => 4
0000010110 => 4
0000101110 => 4
0001011110 => 4
0001101110 => 4
0001110110 => 4
0001111010 => 4
0001111100 => 2
0000000101 => 3
0000001101 => 3
0000011101 => 3
0001111101 => 3
0000001001 => 3
0000010101 => 5
0000101101 => 5
0010110001 => 5
0001100001 => 3
0001000001 => 3
0000111111 => 1
0001110100 => 4
0001101100 => 4
0010011100 => 4
0001011100 => 4
0000111100 => 2
0001101010 => 6
0010011010 => 6
0000111010 => 4
0010100110 => 6
0010010110 => 6
0001010110 => 6
0000110110 => 4
0010001110 => 4
0001101001 => 5
0000110001 => 3
0000010001 => 3
0000001100 => 2
0000011001 => 3
0000110011 => 3
0000110100 => 4
0000000011 => 1
0000011011 => 3
0001101111 => 3
0000110101 => 5
0010000010 => 4
0001000011 => 3
0010011110 => 4
0001010000 => 4
0001000100 => 4
0001010101 => 7
0001001011 => 5
0001100011 => 3
0001110111 => 3
0010000000 => 2
0000000111 => 1
0000001111 => 1
0001111111 => 1
0000001011 => 3
0000010111 => 3
0001011111 => 3
0001111001 => 3
0000011010 => 4
0000101010 => 6
0000100101 => 5
0010010001 => 5
0010000101 => 5
0010010101 => 7
0010010011 => 5
0000101011 => 5
0001000111 => 3
0000100111 => 3
0010010010 => 6
0001001010 => 6
0001001001 => 5
0001000101 => 5
0000100011 => 3
0000100100 => 4
0000100010 => 4
0010110000 => 4
0000011100 => 2
0000001000 => 2
0000101100 => 4
0010101111 => 5
0000101000 => 4
0010001000 => 4
0001001100 => 4
0001000110 => 4
0001100100 => 4
0001100010 => 4
0000100110 => 4
0000110010 => 4
0010010000 => 4
0001010010 => 6
0001000000 => 2
0001011001 => 5
0001100101 => 5
0001110001 => 3
0010011001 => 5
0010100101 => 7
0010101001 => 7
0010011111 => 3
0000111001 => 3
0010001101 => 5
0001001101 => 5
0001010001 => 5
0001010011 => 5
0001111011 => 3
0010011000 => 4
0001011000 => 4
0000100000 => 2
0010001011 => 5
0010000111 => 3
0000010011 => 3
0010001100 => 4
0010000110 => 4
0000110000 => 2
0000100001 => 3
0010100011 => 5
0010100001 => 5
0000111000 => 2
0001101000 => 4
0000010000 => 2
0000101001 => 5
0010100010 => 6
0010001001 => 5
0010000011 => 3
0010001010 => 6
0001110000 => 2
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Created: Jan 26, 2017 at 12:24 by Christian Stump
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Last Updated: Jan 26, 2017 at 12:24 by Christian Stump