Identifier
Identifier
Values
0 => 1
1 => 1
00 => 1
01 => 1
10 => 1
11 => 1
000 => 1
001 => 1
010 => 2
011 => 1
100 => 1
101 => 2
110 => 1
111 => 1
0000 => 1
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 => 1
00000 => 1
00001 => 1
00010 => 2
00011 => 1
00100 => 3
00101 => 3
00110 => 2
00111 => 1
01000 => 2
01001 => 4
01010 => 6
01011 => 3
01100 => 2
01101 => 4
01110 => 2
01111 => 1
10000 => 1
10001 => 2
10010 => 4
10011 => 2
10100 => 3
10101 => 6
10110 => 4
10111 => 2
11000 => 1
11001 => 2
11010 => 3
11011 => 3
11100 => 1
11101 => 2
11110 => 1
11111 => 1
000000 => 1
000001 => 1
000010 => 2
000011 => 1
000100 => 3
000101 => 3
000110 => 2
000111 => 1
001000 => 3
001001 => 5
001010 => 7
001011 => 3
001100 => 3
001101 => 4
001110 => 2
001111 => 1
010000 => 2
010001 => 4
010010 => 8
010011 => 4
010100 => 7
010101 => 11
010110 => 7
010111 => 3
011000 => 2
011001 => 5
011010 => 7
011011 => 5
011100 => 2
011101 => 4
011110 => 2
011111 => 1
100000 => 1
100001 => 2
100010 => 4
100011 => 2
100100 => 5
100101 => 7
100110 => 5
100111 => 2
101000 => 3
101001 => 7
101010 => 11
101011 => 7
101100 => 4
101101 => 8
101110 => 4
101111 => 2
110000 => 1
110001 => 2
110010 => 4
110011 => 3
110100 => 3
110101 => 7
110110 => 5
110111 => 3
111000 => 1
111001 => 2
111010 => 3
111011 => 3
111100 => 1
111101 => 2
111110 => 1
111111 => 1
0000000 => 1
0000001 => 1
0000010 => 2
0000011 => 1
0000100 => 3
0000101 => 3
0000110 => 2
0000111 => 1
0001000 => 4
0001001 => 5
0001010 => 7
0001011 => 3
0001100 => 3
0001101 => 4
0001110 => 2
0001111 => 1
0010000 => 3
0010001 => 6
0010010 => 11
0010011 => 5
0010100 => 10
0010101 => 13
0010110 => 8
0010111 => 3
0011000 => 3
0011001 => 7
0011010 => 9
0011011 => 5
0011100 => 3
0011101 => 4
0011110 => 2
0011111 => 1
0100000 => 2
0100001 => 4
0100010 => 9
0100011 => 4
0100100 => 11
0100101 => 15
0100110 => 10
0100111 => 4
0101000 => 7
0101001 => 16
0101010 => 24
0101011 => 13
0101100 => 9
0101101 => 15
0101110 => 7
0101111 => 3
0110000 => 2
0110001 => 5
0110010 => 10
0110011 => 7
0110100 => 8
0110101 => 16
0110110 => 11
0110111 => 5
0111000 => 2
0111001 => 5
0111010 => 7
0111011 => 6
0111100 => 2
0111101 => 4
0111110 => 2
0111111 => 1
1000000 => 1
1000001 => 2
1000010 => 4
1000011 => 2
1000100 => 6
1000101 => 7
1000110 => 5
1000111 => 2
1001000 => 5
1001001 => 11
1001010 => 16
1001011 => 8
1001100 => 7
1001101 => 10
1001110 => 5
1001111 => 2
1010000 => 3
1010001 => 7
1010010 => 15
1010011 => 9
1010100 => 13
1010101 => 24
1010110 => 16
1010111 => 7
1011000 => 4
1011001 => 10
1011010 => 15
1011011 => 11
1011100 => 4
1011101 => 9
1011110 => 4
1011111 => 2
1100000 => 1
1100001 => 2
1100010 => 4
1100011 => 3
1100100 => 5
1100101 => 9
1100110 => 7
1100111 => 3
1101000 => 3
1101001 => 8
1101010 => 13
1101011 => 10
1101100 => 5
1101101 => 11
1101110 => 6
1101111 => 3
1110000 => 1
1110001 => 2
1110010 => 4
1110011 => 3
1110100 => 3
1110101 => 7
1110110 => 5
1110111 => 4
1111000 => 1
1111001 => 2
1111010 => 3
1111011 => 3
1111100 => 1
1111101 => 2
1111110 => 1
1111111 => 1
00000000 => 1
00000001 => 1
00000010 => 2
00000011 => 1
00000100 => 3
00000101 => 3
00000110 => 2
00000111 => 1
00001000 => 4
00001001 => 5
00001010 => 7
00001011 => 3
00001100 => 3
00001101 => 4
00001110 => 2
00001111 => 1
00010000 => 4
00010001 => 7
00010010 => 12
00010011 => 5
00010100 => 11
00010101 => 13
00010110 => 8
00010111 => 3
00011000 => 4
00011001 => 7
00011010 => 9
00011011 => 5
00011100 => 3
00011101 => 4
00011110 => 2
00011111 => 1
00100000 => 3
00100001 => 6
00100010 => 13
00100011 => 6
00100100 => 16
00100101 => 20
00100110 => 13
00100111 => 5
00101000 => 11
00101001 => 22
00101010 => 31
00101011 => 15
00101100 => 12
00101101 => 17
00101110 => 8
00101111 => 3
00110000 => 3
00110001 => 8
00110010 => 15
00110011 => 9
00110100 => 12
00110101 => 20
00110110 => 13
00110111 => 5
00111000 => 3
00111001 => 7
00111010 => 9
00111011 => 6
00111100 => 3
00111101 => 4
00111110 => 2
00111111 => 1
01000000 => 2
01000001 => 4
01000010 => 9
01000011 => 4
01000100 => 13
01000101 => 16
01000110 => 11
01000111 => 4
01001000 => 12
01001001 => 24
01001010 => 35
01001011 => 17
01001100 => 15
01001101 => 21
01001110 => 10
01001111 => 4
01010000 => 7
01010001 => 17
01010010 => 35
01010011 => 20
01010100 => 31
01010101 => 51
01010110 => 33
01010111 => 13
01011000 => 9
01011001 => 23
01011010 => 32
01011011 => 20
01011100 => 9
01011101 => 16
01011110 => 7
01011111 => 3
01100000 => 2
01100001 => 5
01100010 => 11
01100011 => 7
01100100 => 13
01100101 => 23
01100110 => 17
01100111 => 7
01101000 => 8
01101001 => 21
01101010 => 33
01101011 => 22
01101100 => 13
01101101 => 24
01101110 => 12
01101111 => 5
01110000 => 2
01110001 => 5
01110010 => 10
01110011 => 8
01110100 => 8
01110101 => 17
01110110 => 12
01110111 => 7
01111000 => 2
01111001 => 5
01111010 => 7
01111011 => 6
01111100 => 2
01111101 => 4
01111110 => 2
01111111 => 1
10000000 => 1
10000001 => 2
10000010 => 4
10000011 => 2
10000100 => 6
10000101 => 7
10000110 => 5
10000111 => 2
10001000 => 7
10001001 => 12
10001010 => 17
10001011 => 8
10001100 => 8
10001101 => 10
10001110 => 5
10001111 => 2
10010000 => 5
10010001 => 12
10010010 => 24
10010011 => 13
10010100 => 22
10010101 => 33
10010110 => 21
10010111 => 8
10011000 => 7
10011001 => 17
10011010 => 23
10011011 => 13
10011100 => 7
10011101 => 11
10011110 => 5
10011111 => 2
10100000 => 3
10100001 => 7
10100010 => 16
10100011 => 9
10100100 => 20
10100101 => 32
10100110 => 23
10100111 => 9
10101000 => 13
10101001 => 33
10101010 => 51
10101011 => 31
10101100 => 20
10101101 => 35
10101110 => 17
10101111 => 7
10110000 => 4
10110001 => 10
10110010 => 21
10110011 => 15
10110100 => 17
10110101 => 35
10110110 => 24
10110111 => 12
10111000 => 4
10111001 => 11
10111010 => 16
10111011 => 13
10111100 => 4
10111101 => 9
10111110 => 4
10111111 => 2
11000000 => 1
11000001 => 2
11000010 => 4
11000011 => 3
11000100 => 6
11000101 => 9
11000110 => 7
11000111 => 3
11001000 => 5
11001001 => 13
11001010 => 20
11001011 => 12
11001100 => 9
11001101 => 15
11001110 => 8
11001111 => 3
11010000 => 3
11010001 => 8
11010010 => 17
11010011 => 12
11010100 => 15
11010101 => 31
11010110 => 22
11010111 => 11
11011000 => 5
11011001 => 13
11011010 => 20
11011011 => 16
11011100 => 6
11011101 => 13
11011110 => 6
11011111 => 3
11100000 => 1
11100001 => 2
11100010 => 4
11100011 => 3
11100100 => 5
11100101 => 9
11100110 => 7
11100111 => 4
11101000 => 3
11101001 => 8
11101010 => 13
11101011 => 11
11101100 => 5
11101101 => 12
11101110 => 7
11101111 => 4
11110000 => 1
11110001 => 2
11110010 => 4
11110011 => 3
11110100 => 3
11110101 => 7
11110110 => 5
11110111 => 4
11111000 => 1
11111001 => 2
11111010 => 3
11111011 => 3
11111100 => 1
11111101 => 2
11111110 => 1
11111111 => 1
000000000 => 1
000000001 => 1
000000010 => 2
000000011 => 1
000000100 => 3
000000101 => 3
000000110 => 2
000000111 => 1
000001000 => 4
000001001 => 5
000001010 => 7
000001011 => 3
000001100 => 3
000001101 => 4
000001110 => 2
000001111 => 1
000010000 => 5
000010001 => 7
000010010 => 12
000010011 => 5
000010100 => 11
000010101 => 13
000010110 => 8
000010111 => 3
000011000 => 4
000011001 => 7
000011010 => 9
000011011 => 5
000011100 => 3
000011101 => 4
000011110 => 2
000011111 => 1
000100000 => 4
000100001 => 8
000100010 => 16
000100011 => 7
000100100 => 19
000100101 => 22
000100110 => 14
000100111 => 5
000101000 => 14
000101001 => 24
000101010 => 33
000101011 => 15
000101100 => 13
000101101 => 17
000101110 => 8
000101111 => 3
000110000 => 4
000110001 => 10
000110010 => 17
000110011 => 9
000110100 => 14
000110101 => 20
000110110 => 13
000110111 => 5
000111000 => 4
000111001 => 7
000111010 => 9
000111011 => 6
000111100 => 3
000111101 => 4
000111110 => 2
000111111 => 1
001000000 => 3
001000001 => 6
001000010 => 14
001000011 => 6
001000100 => 20
001000101 => 24
001000110 => 16
001000111 => 6
001001000 => 19
001001001 => 35
001001010 => 50
001001011 => 23
001001100 => 21
001001101 => 28
001001110 => 13
001001111 => 5
001010000 => 11
001010001 => 27
001010010 => 52
001010011 => 27
001010100 => 46
001010101 => 67
001010110 => 42
001010111 => 15
001011000 => 14
001011001 => 31
001011010 => 41
001011011 => 23
001011100 => 12
001011101 => 18
001011110 => 8
001011111 => 3
001100000 => 3
001100001 => 8
001100010 => 18
001100011 => 11
001100100 => 21
001100101 => 34
001100110 => 24
001100111 => 9
001101000 => 13
001101001 => 32
001101010 => 47
001101011 => 27
001101100 => 19
001101101 => 29
001101110 => 14
001101111 => 5
001110000 => 3
001110001 => 8
001110010 => 15
001110011 => 11
001110100 => 12
001110101 => 22
001110110 => 15
001110111 => 7
001111000 => 3
001111001 => 7
001111010 => 9
001111011 => 6
001111100 => 3
001111101 => 4
001111110 => 2
001111111 => 1
010000000 => 2
010000001 => 4
010000010 => 9
010000011 => 4
010000100 => 14
010000101 => 16
010000110 => 11
010000111 => 4
010001000 => 16
010001001 => 28
010001010 => 40
010001011 => 18
010001100 => 18
010001101 => 23
010001110 => 11
010001111 => 4
010010000 => 12
010010001 => 29
010010010 => 57
010010011 => 29
010010100 => 52
010010101 => 75
010010110 => 47
010010111 => 17
010011000 => 17
010011001 => 38
010011010 => 51
010011011 => 28
010011100 => 15
010011101 => 23
010011110 => 10
010011111 => 4
010100000 => 7
010100001 => 17
010100010 => 40
010100011 => 22
010100100 => 50
010100101 => 77
010100110 => 54
010100111 => 20
010101000 => 33
010101001 => 80
010101010 => 120
010101011 => 67
010101100 => 47
010101101 => 75
010101110 => 35
010101111 => 13
010110000 => 9
010110001 => 25
010110010 => 51
010110011 => 34
010110100 => 41
010110101 => 77
010110110 => 51
010110111 => 22
010111000 => 9
010111001 => 25
010111010 => 34
010111011 => 24
010111100 => 9
010111101 => 16
010111110 => 7
010111111 => 3
011000000 => 2
011000001 => 5
011000010 => 11
011000011 => 7
011000100 => 16
011000101 => 25
011000110 => 19
011000111 => 7
011001000 => 14
011001001 => 35
011001010 => 54
011001011 => 31
011001100 => 24
011001101 => 38
011001110 => 19
011001111 => 7
011010000 => 8
011010001 => 22
011010010 => 47
011010011 => 32
011010100 => 42
011010101 => 80
011010110 => 55
011010111 => 24
011011000 => 13
011011001 => 35
011011010 => 51
011011011 => 35
011011100 => 15
011011101 => 28
011011110 => 12
011011111 => 5
011100000 => 2
011100001 => 5
011100010 => 11
011100011 => 8
011100100 => 13
011100101 => 25
011100110 => 19
011100111 => 10
011101000 => 8
011101001 => 22
011101010 => 35
011101011 => 27
011101100 => 14
011101101 => 29
011101110 => 16
011101111 => 7
011110000 => 2
011110001 => 5
011110010 => 10
011110011 => 8
011110100 => 8
011110101 => 17
011110110 => 12
011110111 => 8
011111000 => 2
011111001 => 5
011111010 => 7
011111011 => 6
011111100 => 2
011111101 => 4
011111110 => 2
011111111 => 1
100000000 => 1
100000001 => 2
100000010 => 4
100000011 => 2
100000100 => 6
100000101 => 7
100000110 => 5
100000111 => 2
100001000 => 8
100001001 => 12
100001010 => 17
100001011 => 8
100001100 => 8
100001101 => 10
100001110 => 5
100001111 => 2
100010000 => 7
100010001 => 16
100010010 => 29
100010011 => 14
100010100 => 27
100010101 => 35
100010110 => 22
100010111 => 8
100011000 => 10
100011001 => 19
100011010 => 25
100011011 => 13
100011100 => 8
100011101 => 11
100011110 => 5
100011111 => 2
100100000 => 5
100100001 => 12
100100010 => 28
100100011 => 15
100100100 => 35
100100101 => 51
100100110 => 35
100100111 => 13
100101000 => 24
100101001 => 55
100101010 => 80
100101011 => 42
100101100 => 32
100101101 => 47
100101110 => 22
100101111 => 8
100110000 => 7
100110001 => 19
100110010 => 38
100110011 => 24
100110100 => 31
100110101 => 54
100110110 => 35
100110111 => 14
100111000 => 7
100111001 => 19
100111010 => 25
100111011 => 16
100111100 => 7
100111101 => 11
100111110 => 5
100111111 => 2
101000000 => 3
101000001 => 7
101000010 => 16
101000011 => 9
101000100 => 24
101000101 => 34
101000110 => 25
101000111 => 9
101001000 => 22
101001001 => 51
101001010 => 77
101001011 => 41
101001100 => 34
101001101 => 51
101001110 => 25
101001111 => 9
101010000 => 13
101010001 => 35
101010010 => 75
101010011 => 47
101010100 => 67
101010101 => 120
101010110 => 80
101010111 => 33
101011000 => 20
101011001 => 54
101011010 => 77
101011011 => 50
101011100 => 22
101011101 => 40
101011110 => 17
101011111 => 7
101100000 => 4
101100001 => 10
101100010 => 23
101100011 => 15
101100100 => 28
101100101 => 51
101100110 => 38
101100111 => 17
101101000 => 17
101101001 => 47
101101010 => 75
101101011 => 52
101101100 => 29
101101101 => 57
101101110 => 29
101101111 => 12
101110000 => 4
101110001 => 11
101110010 => 23
101110011 => 18
101110100 => 18
101110101 => 40
101110110 => 28
101110111 => 16
101111000 => 4
101111001 => 11
101111010 => 16
101111011 => 14
101111100 => 4
101111101 => 9
101111110 => 4
101111111 => 2
110000000 => 1
110000001 => 2
110000010 => 4
110000011 => 3
110000100 => 6
110000101 => 9
110000110 => 7
110000111 => 3
110001000 => 7
110001001 => 15
110001010 => 22
110001011 => 12
110001100 => 11
110001101 => 15
110001110 => 8
110001111 => 3
110010000 => 5
110010001 => 14
110010010 => 29
110010011 => 19
110010100 => 27
110010101 => 47
110010110 => 32
110010111 => 13
110011000 => 9
110011001 => 24
110011010 => 34
110011011 => 21
110011100 => 11
110011101 => 18
110011110 => 8
110011111 => 3
110100000 => 3
110100001 => 8
110100010 => 18
110100011 => 12
110100100 => 23
110100101 => 41
110100110 => 31
110100111 => 14
110101000 => 15
110101001 => 42
110101010 => 67
110101011 => 46
110101100 => 27
110101101 => 52
110101110 => 27
110101111 => 11
110110000 => 5
110110001 => 13
110110010 => 28
110110011 => 21
110110100 => 23
110110101 => 50
110110110 => 35
110110111 => 19
110111000 => 6
110111001 => 16
110111010 => 24
110111011 => 20
110111100 => 6
110111101 => 14
110111110 => 6
110111111 => 3
111000000 => 1
111000001 => 2
111000010 => 4
111000011 => 3
111000100 => 6
111000101 => 9
111000110 => 7
111000111 => 4
111001000 => 5
111001001 => 13
111001010 => 20
111001011 => 14
111001100 => 9
111001101 => 17
111001110 => 10
111001111 => 4
111010000 => 3
111010001 => 8
111010010 => 17
111010011 => 13
111010100 => 15
111010101 => 33
111010110 => 24
111010111 => 14
111011000 => 5
111011001 => 14
111011010 => 22
111011011 => 19
111011100 => 7
111011101 => 16
111011110 => 8
111011111 => 4
111100000 => 1
111100001 => 2
111100010 => 4
111100011 => 3
111100100 => 5
111100101 => 9
111100110 => 7
111100111 => 4
111101000 => 3
111101001 => 8
111101010 => 13
111101011 => 11
111101100 => 5
111101101 => 12
111101110 => 7
111101111 => 5
111110000 => 1
111110001 => 2
111110010 => 4
111110011 => 3
111110100 => 3
111110101 => 7
111110110 => 5
111110111 => 4
111111000 => 1
111111001 => 2
111111010 => 3
111111011 => 3
111111100 => 1
111111101 => 2
111111110 => 1
111111111 => 1
0000000000 => 1
0000000001 => 1
0000000010 => 2
0000000011 => 1
0000000100 => 3
0000000101 => 3
0000000110 => 2
0000000111 => 1
0000001000 => 4
0000001001 => 5
0000001010 => 7
0000001011 => 3
0000001100 => 3
0000001101 => 4
0000001110 => 2
0000001111 => 1
0000010000 => 5
0000010001 => 7
0000010010 => 12
0000010011 => 5
0000010100 => 11
0000010101 => 13
0000010110 => 8
0000010111 => 3
0000011000 => 4
0000011001 => 7
0000011010 => 9
0000011011 => 5
0000011100 => 3
0000011101 => 4
0000011110 => 2
0000011111 => 1
0000100000 => 5
0000100001 => 9
0000100010 => 17
0000100011 => 7
0000100100 => 20
0000100101 => 22
0000100110 => 14
0000100111 => 5
0000101000 => 15
0000101001 => 24
0000101010 => 33
0000101011 => 15
0000101100 => 13
0000101101 => 17
0000101110 => 8
0000101111 => 3
0000110000 => 5
0000110001 => 10
0000110010 => 17
0000110011 => 9
0000110100 => 14
0000110101 => 20
0000110110 => 13
0000110111 => 5
0000111000 => 4
0000111001 => 7
0000111010 => 9
0000111011 => 6
0000111100 => 3
0000111101 => 4
0000111110 => 2
0000111111 => 1
0001000000 => 4
0001000001 => 8
0001000010 => 18
0001000011 => 8
0001000100 => 25
0001000101 => 29
0001000110 => 19
0001000111 => 7
0001001000 => 24
0001001001 => 41
0001001010 => 57
0001001011 => 25
0001001100 => 24
0001001101 => 30
0001001110 => 14
0001001111 => 5
0001010000 => 15
0001010001 => 33
0001010010 => 60
0001010011 => 29
0001010100 => 53
0001010101 => 71
0001010110 => 44
0001010111 => 15
0001011000 => 17
0001011001 => 33
0001011010 => 43
0001011011 => 23
0001011100 => 13
0001011101 => 18
0001011110 => 8
0001011111 => 3
0001100000 => 4
0001100001 => 11
0001100010 => 23
0001100011 => 13
0001100100 => 26
0001100101 => 38
0001100110 => 26
0001100111 => 9
0001101000 => 17
0001101001 => 36
0001101010 => 51
0001101011 => 27
0001101100 => 21
0001101101 => 29
0001101110 => 14
0001101111 => 5
0001110000 => 4
0001110001 => 10
0001110010 => 17
0001110011 => 11
0001110100 => 14
0001110101 => 22
0001110110 => 15
0001110111 => 7
0001111000 => 4
0001111001 => 7
0001111010 => 9
0001111011 => 6
0001111100 => 3
0001111101 => 4
0001111110 => 2
0001111111 => 1
0010000000 => 3
0010000001 => 6
0010000010 => 14
0010000011 => 6
0010000100 => 22
0010000101 => 25
0010000110 => 17
0010000111 => 6
0010001000 => 25
0010001001 => 43
0010001010 => 61
0010001011 => 27
0010001100 => 27
0010001101 => 34
0010001110 => 16
0010001111 => 6
0010010000 => 20
0010010001 => 45
0010010010 => 86
0010010011 => 42
0010010100 => 78
0010010101 => 107
0010010110 => 66
0010010111 => 23
0010011000 => 26
0010011001 => 54
0010011010 => 71
0010011011 => 37
0010011100 => 21
0010011101 => 30
0010011110 => 13
0010011111 => 5
0010100000 => 11
0010100001 => 28
0010100010 => 64
0010100011 => 34
0010100100 => 78
0010100101 => 113
0010100110 => 77
0010100111 => 27
0010101000 => 53
0010101001 => 117
0010101010 => 169
0010101011 => 87
0010101100 => 67
0010101101 => 96
0010101110 => 44
0010101111 => 15
0010110000 => 14
0010110001 => 39
click to show generating function       
Description
The number of standard Young tableaux whose descent set is the binary word.
A descent in a standard Young tableau is an entry $i$ such that $i+1$ appears in a lower row in English notation.
For example, the tableaux $[[1,2,4],[3]]$ and $[[1,2],[3,4]]$ are those with descent set $\{2\}$, corresponding to the binary word $010$.
Code
def statistic(w):
    D = [i+1 for i in range(len(w)) if w[i]==1]
    return len([T for T in StandardTableaux(len(w)+1)
                if T.standard_descents() == D])

Created
Jun 15, 2017 at 08:07 by Martin Rubey
Updated
Jun 15, 2017 at 08:07 by Martin Rubey