A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 57 semigroups of order six, all of which generate the variety V[2727]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-88d603c5fe73e956 in the data of the bases-min seal.
Certified for
[6, 2727] [6, 2728] [6, 2729] [6, 2730] [6, 2732] [6, 2733] [6, 2734] [6, 2735] [6, 2739] [6, 2744] [6, 2746] [6, 2747] [6, 2748] [6, 2751] [6, 2756] [6, 2758] [6, 2784] [6, 5209] [6, 5213] [6, 5214] [6, 5215] [6, 5218] [6, 5220] [6, 5224] [6, 5225] [6, 5226] [6, 5229] [6, 5236] [6, 5264] [6, 5452] [6, 5456] [6, 5606] [6, 5608] [6, 5609] [6, 5610] [6, 5616] [6, 5618] [6, 5657] [6, 5658] [6, 5666] [6, 5667] [6, 5707] [6, 5709] [6, 9300] [6, 9315] [6, 9316] [6, 9317] [6, 9320] [6, 9382] [6, 9445] [6, 9447] [6, 9464] [6, 9465] [6, 9482] [6, 9575] [6, 9599] [6, 9621]
The identities
- x³ ≈ x⁴
- xyx ≈ yx²
- x²y² ≈ xy²x
- xyz ≈ yxz