A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 37 semigroups of order six, all of which generate the variety V[851]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-332df911474f1ca1 in the data of the bases-min seal.
Certified for
[6, 851] [6, 855] [6, 859] [6, 867] [6, 873] [6, 876] [6, 879] [6, 2223] [6, 2226] [6, 2229] [6, 2231] [6, 2509] [6, 2514] [6, 2518] [6, 2527] [6, 2529] [6, 2540] [6, 2544] [6, 2547] [6, 2549] [6, 2550] [6, 2553] [6, 2555] [6, 2559] [6, 2560] [6, 2562] [6, 2563] [6, 4831] [6, 5082] [6, 5085] [6, 5095] [6, 5099] [6, 5102] [6, 5105] [6, 5106] [6, 5109] [6, 5112]
The identities
- xy ≈ yx
- x²y ≈ xy²
- xyzt ≈ uxyzt