Computing witnesses for centralising monoids on a three-element set
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
International Conference on Formal Concept Analysis (ICFCA2023)
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
We use a formal concept theoretic approach to computationally validate the classification of all 192 centralising monoids on three-element sets by Machida and Rosenberg. We determine a manageable finite (and row-reduced) context the intents of which are exactly all centralising monoids on {0,1,2}. As an advantage of our method, we are able to compute a list with a witness for each of the 192 monoids, which has not been available to date and allows for an immediate verification of the figure 192 as a lower bound for the number of centralising monoids. We also confirm that the 192 centralising monoids split into 48 conjugacy classes and we provide a list of all conjugacy types including witnesses.