Unary operations giving co-atoms of K₁=(OA⁽¹⁾,OA⁽¹⁾,⊥) classified into
conjugacy classes
(the numbers used to identify the operations refer to line numbers in the file 49_max_monoids_witn_1_unary_op.txt)
  3 = conj(  2, (23))
  6 = conj(  4, (23))
  7 = conj(  2, (123))
  8 = conj(  4, (12))
  9 = conj(  5, (12))
 10 = conj(  4, (321))
 11 = conj(  2, (0123))
 12 = conj(  5, (012))
 13 = conj(  5, (321))
 14 = conj(  5, (0132))
 15 = conj(  5, (02)(13))
 17 = conj(  5, (0312))
 18 = conj( 16, (321))
 19 = conj(  4, (13))
 20 = conj(  2, (023))
 21 = conj(  5, (02))
 22 = conj(  4, (123))
 23 = conj( 16, (12))
 24 = conj(  5, (320))
 25 = conj(  2, (03))
 26 = conj( 16, (02)(13))
 28 = conj(  1, (01))
 29 = conj(  2, (01))
 30 = conj(  2, (01)(23))
 31 = conj(  4, (01))
 32 = conj(  5, (01))
 33 = conj(  4, (01)(23))
 34 = conj( 16, (0132))
 35 = conj(  4, (013))
 36 = conj(  2, (0231))
 37 = conj(  5, (210))
 38 = conj(  1, (210))
 39 = conj(  2, (210))
 40 = conj( 27, (12))
 41 = conj(  4, (0231))
 42 = conj(  4, (0123))
 43 = conj( 16, (012))
 44 = conj(  5, (0321))
 45 = conj(  2, (310))
 46 = conj( 27, (321))
 47 = conj(  4, (023))
 48 = conj(  2, (0321))
 49 = conj(  1, (0321))
List of (line numbers 1 <= i <= 49 of) representatives up to conjugacy:
1 2 4 5 16 27 
 1 = 0000 = f0   gives a maximal monoid. It is a retraction with im = 0.
 2 = 0003 = f3   gives a maximal monoid. It is a retraction with im = 03.
 4 = 0022 = f10  gives a maximal monoid. It is a retraction with im = 02.
 5 = 0023 = f11  gives a maximal monoid. It is a retraction with im = 023.
16 = 0132 = f30  gives a maximal monoid. It is a permutation of order 2. (23)
27 = 1032 = f78  gives a maximal monoid. It is a permutation of order 2. (01)(23)
