A certified basis of 5 identities
This list of identities is a basis, proved in Lean, of 44 semigroups of order six, all of which generate the variety V[7648]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-57362025c90ab433 in the data of the bases-min seal.
Certified for
[6, 7648] [6, 7667] [6, 8351] [6, 8359] [6, 8452] [6, 8466] [6, 8474] [6, 8494] [6, 10609] [6, 10624] [6, 11256] [6, 11270] [6, 11505] [6, 12753] [6, 12772] [6, 12878] [6, 12884] [6, 13126] [6, 13134] [6, 13229] [6, 13273] [6, 13295] [6, 13306] [6, 13317] [6, 13457] [6, 13478] [6, 13526] [6, 13533] [6, 13537] [6, 13657] [6, 13667] [6, 13683] [6, 13688] [6, 13712] [6, 13715] [6, 13722] [6, 13725] [6, 13731] [6, 13732] [6, 13735] [6, 13802] [6, 13996] [6, 14181] [6, 14261]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- x²y² ≈ xyxy
- x²yz ≈ xyxz