A certified basis of 6 identities
This list of identities is a basis, proved in Lean, of 74 semigroups of order six, all of which generate the variety V[3305]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-104f179028db934a in the data of the bases-min seal.
Certified for
[6, 3305] [6, 3309] [6, 3313] [6, 3330] [6, 3341] [6, 3345] [6, 3353] [6, 3389] [6, 3395] [6, 3447] [6, 3449] [6, 3512] [6, 3573] [6, 6034] [6, 6037] [6, 6040] [6, 6123] [6, 6124] [6, 6132] [6, 6133] [6, 6141] [6, 6186] [6, 6215] [6, 6261] [6, 6336] [6, 6337] [6, 6412] [6, 7314] [6, 7339] [6, 7347] [6, 7362] [6, 7445] [6, 7449] [6, 7450] [6, 7456] [6, 7464] [6, 7510] [6, 7528] [6, 7552] [6, 7568] [6, 7603] [6, 7626] [6, 7650] [6, 7651] [6, 7708] [6, 7711] [6, 7714] [6, 8621] [6, 8632] [6, 8722] [6, 9856] [6, 10043] [6, 10107] [6, 10111] [6, 10126] [6, 10259] [6, 10293] [6, 10297] [6, 10300] [6, 10495] [6, 10503] [6, 10520] [6, 10523] [6, 10525] [6, 10540] [6, 10573] [6, 10594] [6, 10612] [6, 10613] [6, 10719] [6, 11134] [6, 11420] [6, 11535] [6, 11653]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- x²y² ≈ xyx
- xy²z ≈ xyz
- xyzx ≈ xzyx
- xyzy ≈ xzy²