A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 41 semigroups of order six, all of which generate the variety V[5959]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-a3d1b3009c0de8e2 in the data of the bases-min seal.
Certified for
[6, 5959] [6, 5983] [6, 6007] [6, 6009] [6, 6837] [6, 6980] [6, 8822] [6, 8833] [6, 8907] [6, 8918] [6, 8972] [6, 8983] [6, 9048] [6, 9059] [6, 9853] [6, 9879] [6, 10183] [6, 10195] [6, 10199] [6, 10216] [6, 10364] [6, 10370] [6, 10373] [6, 10376] [6, 10383] [6, 10388] [6, 10389] [6, 10392] [6, 10394] [6, 10398] [6, 10400] [6, 10402] [6, 10405] [6, 10407] [6, 10408] [6, 10676] [6, 10681] [6, 11641] [6, 11723] [6, 11748] [6, 11769]
The identities
- x³y ≈ xy
- x²y³ ≈ xyx