A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 38 semigroups of order six, all of which generate the variety V[7631]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-dfccf083bb302aa5 in the data of the bases-min seal.
Certified for
[6, 7631] [6, 7671] [6, 8335] [6, 8363] [6, 8434] [6, 8478] [6, 8491] [6, 8495] [6, 10598] [6, 10630] [6, 11247] [6, 11436] [6, 11543] [6, 12750] [6, 12754] [6, 12769] [6, 13123] [6, 13127] [6, 13135] [6, 13217] [6, 13233] [6, 13262] [6, 13445] [6, 13461] [6, 13482] [6, 13493] [6, 13545] [6, 13634] [6, 13661] [6, 13669] [6, 13741] [6, 13744] [6, 13746] [6, 13984] [6, 14000] [6, 14154] [6, 14168] [6, 14266]
The identities
- xy ≈ xy²
- xyz ≈ xzyz
- x²yz ≈ xyxz