Mike Behrisch, Leon Renkin,
"Computing witnesses for centralising monoids on a three-element set"
, in Dominik Dürrschnabel and Domingo López-Rodríguez: Formal Concept Analysis ? 17th International Conference, ICFCA 2023, Kassel, Germany, July 17?21, 2023, Proceedings, Serie Lecture Notes in Artificial Intelligence (LNAI), Vol. 13934, Springer, Cham, Seite(n) 109?126, 7-2023, ISBN: 978-3-031-35949-1
Original Titel:
Computing witnesses for centralising monoids on a three-element set
Sprache des Titels:
Englisch
Original Buchtitel:
Formal Concept Analysis ? 17th International Conference, ICFCA 2023, Kassel, Germany, July 17?21, 2023, Proceedings
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.
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