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Statistic identifier: St000529
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Collection: Binary words
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Description: The number of permutations whose descent word is the given binary word.
This is the sizes of the preimages of the map [[Mp00109]].
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References:
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Code:
from collections import defaultdict
def word(pi):
w = [0]*(len(pi)-1)
for i in pi.descents():
w[i] = 1
return Words([0,1])(w)
@cached_function
def preimages(n):
D = defaultdict(int)
for pi in Permutations(n):
D[word(pi)] += 1
return D
def statistic(word):
return preimages(len(word)+Integer(1))[word]
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Statistic values:
0 => 1
1 => 1
00 => 1
01 => 2
10 => 2
11 => 1
000 => 1
001 => 3
010 => 5
011 => 3
100 => 3
101 => 5
110 => 3
111 => 1
0000 => 1
0001 => 4
0010 => 9
0011 => 6
0100 => 9
0101 => 16
0110 => 11
0111 => 4
1000 => 4
1001 => 11
1010 => 16
1011 => 9
1100 => 6
1101 => 9
1110 => 4
1111 => 1
00000 => 1
00001 => 5
00010 => 14
00011 => 10
00100 => 19
00101 => 35
00110 => 26
00111 => 10
01000 => 14
01001 => 40
01010 => 61
01011 => 35
01100 => 26
01101 => 40
01110 => 19
01111 => 5
10000 => 5
10001 => 19
10010 => 40
10011 => 26
10100 => 35
10101 => 61
10110 => 40
10111 => 14
11000 => 10
11001 => 26
11010 => 35
11011 => 19
11100 => 10
11101 => 14
11110 => 5
11111 => 1
000000 => 1
000001 => 6
000010 => 20
000011 => 15
000100 => 34
000101 => 64
000110 => 50
000111 => 20
001000 => 34
001001 => 99
001010 => 155
001011 => 90
001100 => 71
001101 => 111
001110 => 55
001111 => 15
010000 => 20
010001 => 78
010010 => 169
010011 => 111
010100 => 155
010101 => 272
010110 => 181
010111 => 64
011000 => 50
011001 => 132
011010 => 181
011011 => 99
011100 => 55
011101 => 78
011110 => 29
011111 => 6
100000 => 6
100001 => 29
100010 => 78
100011 => 55
100100 => 99
100101 => 181
100110 => 132
100111 => 50
101000 => 64
101001 => 181
101010 => 272
101011 => 155
101100 => 111
101101 => 169
101110 => 78
101111 => 20
110000 => 15
110001 => 55
110010 => 111
110011 => 71
110100 => 90
110101 => 155
110110 => 99
110111 => 34
111000 => 20
111001 => 50
111010 => 64
111011 => 34
111100 => 15
111101 => 20
111110 => 6
111111 => 1
0000000 => 1
0000001 => 7
0000010 => 27
0000011 => 21
0000100 => 55
0000101 => 105
0000110 => 85
0000111 => 35
0001000 => 69
0001001 => 203
0001010 => 323
0001011 => 189
0001100 => 155
0001101 => 245
0001110 => 125
0001111 => 35
0010000 => 55
0010001 => 217
0010010 => 477
0010011 => 315
0010100 => 449
0010101 => 791
0010110 => 531
0010111 => 189
0011000 => 155
0011001 => 413
0011010 => 573
0011011 => 315
0011100 => 181
0011101 => 259
0011110 => 99
0011111 => 21
0100000 => 27
0100001 => 133
0100010 => 365
0100011 => 259
0100100 => 477
0100101 => 875
0100110 => 643
0100111 => 245
0101000 => 323
0101001 => 917
0101010 => 1385
0101011 => 791
0101100 => 573
0101101 => 875
0101110 => 407
0101111 => 105
0110000 => 85
0110001 => 315
0110010 => 643
0110011 => 413
0110100 => 531
0110101 => 917
0110110 => 589
0110111 => 203
0111000 => 125
0111001 => 315
0111010 => 407
0111011 => 217
0111100 => 99
0111101 => 133
0111110 => 41
0111111 => 7
1000000 => 7
1000001 => 41
1000010 => 133
1000011 => 99
1000100 => 217
1000101 => 407
1000110 => 315
1000111 => 125
1001000 => 203
1001001 => 589
1001010 => 917
1001011 => 531
1001100 => 413
1001101 => 643
1001110 => 315
1001111 => 85
1010000 => 105
1010001 => 407
1010010 => 875
1010011 => 573
1010100 => 791
1010101 => 1385
1010110 => 917
1010111 => 323
1011000 => 245
1011001 => 643
1011010 => 875
1011011 => 477
1011100 => 259
1011101 => 365
1011110 => 133
1011111 => 27
1100000 => 21
1100001 => 99
1100010 => 259
1100011 => 181
1100100 => 315
1100101 => 573
1100110 => 413
1100111 => 155
1101000 => 189
1101001 => 531
1101010 => 791
1101011 => 449
1101100 => 315
1101101 => 477
1101110 => 217
1101111 => 55
1110000 => 35
1110001 => 125
1110010 => 245
1110011 => 155
1110100 => 189
1110101 => 323
1110110 => 203
1110111 => 69
1111000 => 35
1111001 => 85
1111010 => 105
1111011 => 55
1111100 => 21
1111101 => 27
1111110 => 7
1111111 => 1
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Created: Jun 08, 2016 at 13:19 by Christian Stump
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Last Updated: Jun 08, 2016 at 13:19 by Christian Stump