A certified basis of 10 identities
This list of identities is a basis, proved in Lean, of 14 semigroups of order six, all of which generate the variety V[2617]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-b55a878966dd3167 in the data of the bases-min seal.
Certified for
[6, 2617] [6, 2618] [6, 2619] [6, 2640] [6, 2659] [6, 2660] [6, 2685] [6, 2686] [6, 5196] [6, 5426] [6, 5573] [6, 5575] [6, 5578] [6, 5701]
The identities
- x³ ≈ x⁴
- xyx ≈ yxy
- x³y ≈ x²y
- x²yx ≈ xyx
- x²y² ≈ xy²
- xyx ≈ xy³
- xyx ≈ xy²x²
- x²yz ≈ xyz
- xyzx ≈ xyzy
- xyz² ≈ yxz²