Permutations without reversed sequences in Python

Question

I would like to generate a list of all permutations of 4 digits where :

• All 4 digits are always present
• Two reversed sequences are the same solution. For example. (1,2,3,4) = (4,3,2,1)

I would like to know:

• What do you call this kind of permutations.
• If it is possible to generate this list in one step. Below there is an example that generates it in two steps.

import itertools
inp_list = range(1, 5)

# 1. Create the list of all permutations.
permutations = list(itertools.permutations(inp_list))

# 2. Remove sequences that are the reverse of another.
for _p in permutations[::-1]:
    if _p[::-1] in permutations:
        permutations.remove(_p)

for _p in permutations:
    print("\t".join(map(str, _p)))

Answer 1

You could just use the smaller one of each reversal pair:

from itertools import permutations

for p in permutations(range(1, 5)):
    if p < p[::-1]:
        print(*p)

Output:

1 2 3 4
1 2 4 3
1 3 2 4
1 3 4 2
1 4 2 3
1 4 3 2
2 1 3 4
2 1 4 3
2 3 1 4
2 4 1 3
3 1 2 4
3 2 1 4