A certified basis of 9 identities
This list of identities is a basis, proved in Lean, of 102 semigroups of order six, all of which generate the variety V[3307]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-7d2db22f70eaf6a0 in the data of the bases-min seal.
Certified for
[6, 3307] [6, 3311] [6, 3315] [6, 3336] [6, 3348] [6, 3350] [6, 3357] [6, 3391] [6, 3398] [6, 3445] [6, 3451] [6, 3453] [6, 3514] [6, 3516] [6, 3518] [6, 3567] [6, 3576] [6, 3580] [6, 3606] [6, 3610] [6, 3612] [6, 3615] [6, 3657] [6, 3659] [6, 3661] [6, 3713] [6, 3715] [6, 3717] [6, 3886] [6, 3891] [6, 3893] [6, 3896] [6, 3913] [6, 3916] [6, 6127] [6, 6128] [6, 6144] [6, 6145] [6, 6227] [6, 6273] [6, 6332] [6, 6345] [6, 6346] [6, 6496] [6, 6567] [6, 7316] [6, 7341] [6, 7348] [6, 7364] [6, 7447] [6, 7452] [6, 7457] [6, 7466] [6, 7512] [6, 7532] [6, 7555] [6, 7571] [6, 7597] [6, 7607] [6, 7642] [6, 7661] [6, 7662] [6, 7700] [6, 7703] [6, 7723] [6, 7725] [6, 7728] [6, 7747] [6, 7763] [6, 7768] [6, 7777] [6, 7861] [6, 7876] [6, 8300] [6, 8309] [6, 8345] [6, 8353] [6, 8354] [6, 8518] [6, 8521] [6, 8526] [6, 8528] [6, 8531] [6, 8623] [6, 8635] [6, 8652] [6, 8687] [6, 8726] [6, 8736] [6, 10045] [6, 10109] [6, 10130] [6, 10261] [6, 10295] [6, 10304] [6, 10524] [6, 10723] [6, 10758] [6, 11183] [6, 11470] [6, 11562] [6, 11564]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²yz ≈ xyxz
- xyzx ≈ xzyx
- xyzy ≈ xzy²
- xyzt ≈ xzyt