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Identifier
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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Description
The number of permutations whose descent word is the given binary word.
This is the sizes of the preimages of the map Mp00109descent word.
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]
Created
Jun 08, 2016 at 13:19 by Christian Stump
Updated
Jun 08, 2016 at 13:19 by Christian Stump