A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 54 semigroups of order six, all of which generate the variety V[4117]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-967a20ceb407000b in the data of the bases-min seal.
Certified for
[6, 4117] [6, 4224] [6, 4323] [6, 5932] [6, 6835] [6, 6877] [6, 6978] [6, 7020] [6, 8819] [6, 8903] [6, 8915] [6, 8929] [6, 8934] [6, 8936] [6, 8942] [6, 8944] [6, 8945] [6, 8946] [6, 8969] [6, 9044] [6, 9056] [6, 9070] [6, 9075] [6, 9077] [6, 9083] [6, 9085] [6, 9086] [6, 9087] [6, 9849] [6, 9962] [6, 10178] [6, 10193] [6, 10197] [6, 10201] [6, 10214] [6, 10222] [6, 10223] [6, 10227] [6, 10229] [6, 10230] [6, 10232] [6, 10233] [6, 10675] [6, 10679] [6, 10685] [6, 11623] [6, 11715] [6, 11743] [6, 11764] [6, 11811] [6, 11814] [6, 11816] [6, 11845] [6, 11851]
The identities
- x³y ≈ xy
- x²y ≈ xyx
- xy ≈ xy³
- xy ≈ xyxyxy