A certified basis of 7 identities
This list of identities is a basis, proved in Lean, of 64 semigroups of order six, all of which generate the variety V[3319]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-c951cb7c1160f48e in the data of the bases-min seal.
Certified for
[6, 3319] [6, 3321] [6, 3323] [6, 3331] [6, 3333] [6, 3342] [6, 3344] [6, 3354] [6, 3396] [6, 3537] [6, 3547] [6, 3559] [6, 3560] [6, 3570] [6, 3571] [6, 3574] [6, 3582] [6, 3583] [6, 3589] [6, 3590] [6, 3594] [6, 3595] [6, 3596] [6, 3599] [6, 3603] [6, 3604] [6, 3607] [6, 3611] [6, 3736] [6, 3906] [6, 3914] [6, 6242] [6, 6243] [6, 6244] [6, 6245] [6, 6262] [6, 6263] [6, 6265] [6, 6266] [6, 6276] [6, 6278] [6, 7547] [6, 7553] [6, 7557] [6, 7561] [6, 7563] [6, 7569] [6, 7595] [6, 7600] [6, 7604] [6, 7680] [6, 7681] [6, 7684] [6, 7685] [6, 7686] [6, 7687] [6, 7709] [6, 7712] [6, 7717] [6, 8627] [6, 8633] [6, 10121] [6, 10127] [6, 10301]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²y² ≈ yx²y
- x²yz ≈ xyxz