A certified basis of 6 identities
This list of identities is a basis, proved in Lean, of 34 semigroups of order six, all of which generate the variety V[3467]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-942765eff031c954 in the data of the bases-min seal.
Certified for
[6, 3467] [6, 3469] [6, 3494] [6, 3522] [6, 3536] [6, 3672] [6, 3673] [6, 3677] [6, 3690] [6, 3723] [6, 3735] [6, 3748] [6, 3751] [6, 3755] [6, 3783] [6, 3784] [6, 3786] [6, 3833] [6, 3835] [6, 6364] [6, 6461] [6, 7885] [6, 7903] [6, 7921] [6, 7965] [6, 8110] [6, 8112] [6, 8178] [6, 8250] [6, 8658] [6, 10730] [6, 10770] [6, 10881] [6, 11572]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- xyxy ≈ xy²x
- xyxy ≈ yx²y
- xyzx ≈ xzyx