A certified basis of 10 identities
This list of identities is a basis, proved in Lean, of 71 semigroups of order six, all of which generate the variety V[1029]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-ba855756dc4cb877 in the data of the bases-min seal.
Certified for
[6, 1029] [6, 1030] [6, 1032] [6, 1033] [6, 1036] [6, 1037] [6, 1047] [6, 1048] [6, 1049] [6, 1073] [6, 1088] [6, 1090] [6, 1091] [6, 1092] [6, 1094] [6, 1095] [6, 1097] [6, 1103] [6, 1106] [6, 1107] [6, 1108] [6, 1148] [6, 1150] [6, 1152] [6, 1156] [6, 1159] [6, 1160] [6, 3000] [6, 3002] [6, 3036] [6, 3457] [6, 3458] [6, 3461] [6, 3462] [6, 3485] [6, 3486] [6, 3488] [6, 3489] [6, 3524] [6, 3539] [6, 3546] [6, 3548] [6, 3585] [6, 3591] [6, 3598] [6, 3605] [6, 3609] [6, 3665] [6, 3668] [6, 3899] [6, 3903] [6, 3912] [6, 3981] [6, 3982] [6, 3991] [6, 6063] [6, 6064] [6, 6101] [6, 6102] [6, 6253] [6, 6264] [6, 6274] [6, 6297] [6, 6559] [6, 6568] [6, 6672] [6, 6673] [6, 6681] [6, 6688] [6, 6694] [6, 6741]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²y² ≈ yx²y
- x²yz ≈ xyxz
- xyzx ≈ xzyx
- xyzy ≈ xzy²
- xyzt ≈ xzyt