permutations of varying length

permutations of varying length - Printable Version

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permutations of varying length - Skaperen - Feb-15-2022

i need to create permutations of N letters. but i also need all lengths in range(1,N+1), N just happens to also be the number of letters to be permuted? what is this kind of permutation called? is there a way to do this in itertools? or do i need to chain a bunch of permute() iterators of varying length? i know a way to do this but i am unsure of the best way in Python.

RE: permutations of varying length - Gribouillis - Feb-17-2022

These kinds of permutations are called «Arrangements» in classical mathematical literature (although there may be more modern terms to refer to them) See the paragraph about k-permutations of n here https://en.wikipedia.org/wiki/Permutation#k-permutations_of_n (note that these are only the 'restricted partial premutations' in https://en.wikipedia.org/wiki/Partial_permutation#Restricted_partial_permutations)

The following piece of code should do the trick

s = "abcde"                               
n = len(s)                                 
seq = (a for i in range(1, n+1) for c in itt.combinations(s, i) for a in itt.permutations(c, i))                                       
                                           
for x in seq:                             
    print(x)

RE: permutations of varying length - Skaperen - Feb-18-2022

i was using chain().

if there is a more modern term, i'd expect wikipedia to have it.

i'm also doing this as a combination of two sets of permutations to make a variety of command symlinks. here is the code i have done, so far:

from itertools import chain, permutations

s1 = 'eio' # characters for name base
s2 = 'al'  # characters for name suffix

# combine all permutations of base and suffix
# and also without a suffix

# these combinations are excluded
ex = ('e','eio')

def vlp(s):
    """Varying length permutations chained together, 1 to max (inclusive)."""
    return chain(*[permutations(s,n)for n in range(1,len(s)+1)])

a = [x for x in vlp(s1)]
b = [()] + [x for x in vlp(s2)] # include [()] so there is an empty case in suffixes
p = [x+y for x in a for y in b] # join all combinations including the empty suffix
n = [''.join(x) for x in p if ''.join(x) not in ex] # make strings and do excludes

# print all the nammes and how many
print(' '.join(sorted(n)))
print(len(n))

i'd like to find a way to do that comprehension in line 19 coding ''.join(x) only once.

RE: permutations of varying length - Gribouillis - Feb-18-2022

This perhaps?

import itertools as itt

s1 = 'eio' # characters for name base
s2 = 'al'  # characters for name suffix
 
# combine all permutations of base and suffix
# and also without a suffix
 
# these combinations are excluded
ex = ('e', 'eio')
 
def vlp(s, start=0):
    """Varying length permutations chained together, start to max (inclusive)."""
    return itt.chain.from_iterable(
        itt.permutations(s, n) for n in range(start, len(s) + 1))

n = [z for z in (
        ''.join(x + y) for x, y in itt.product(
                        vlp(s1, 1), vlp(s2))) if z not in ex]
 
# print all the nammes and how many
print(' '.join(sorted(n)))
print(len(n))

RE: permutations of varying length - Skaperen - Feb-19-2022

it works, but i will need to study it a while to understand all the changes.