A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 33 semigroups of order six, all of which generate the variety V[9090]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-efbf7902d1402699 in the data of the bases-min seal.
Certified for
[6, 9090] [6, 9100] [6, 9110] [6, 9111] [6, 11927] [6, 11930] [6, 14898] [6, 14902] [6, 14904] [6, 14927] [6, 14929] [6, 14942] [6, 14945] [6, 14946] [6, 14952] [6, 14953] [6, 14955] [6, 14956] [6, 14957] [6, 14959] [6, 14969] [6, 14972] [6, 14982] [6, 14983] [6, 15914] [6, 15916] [6, 15917] [6, 15921] [6, 15925] [6, 15935] [6, 15936] [6, 15946] [6, 15947]
The identities
- xy ≈ yx
- x⁴y ≈ xy
- xy ≈ xy⁴
- xy ≈ xyxyxyxy