Parity0123Premutations.txt

Parity of 0123 permutations:
 - 4! = 24 sequences

Rules:
 - a shift left changes parity
 - sequence reversal is the same parity
 - single swap changes parity
 
0123 even 3210 even
1230 odd  0321 odd
2301 even 1032 even
3012 odd  2103 odd

- swap 01 rotate left to start next block
0231 even 1320 even
2310 odd  0132 odd
3102 even 2013 even
1023 odd  3201 odd

- swap 03 rotate left to start next block
1203 even 3021 even
2031 odd  1302 odd
0312 even 2130 even
3120 odd  0213 odd

1. There are really only 6 even and odd sequences - the others are mirrors.
2. Another way to start the next blocks from 0123:

• pin 0 and rotate left 123 -> 0231
• pin 3 and rotate left 012 -> 1203