Record link: 
http://hdl.handle.net/20.500.12708/187745
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Title: 
Computing Witnesses for Centralising Monoids on a Three-Element Set
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Citation: 
Behrisch, M., & Renkin, L. (2023). Computing Witnesses for Centralising Monoids on a Three-Element Set. In D. Dürrschnabel & D. López Rodríguez (Eds.), Formal Concept Analysis: 17th International Conference, ICFCA 2023, Kassel, Germany, July 17–21, 2023, Proceedings (pp. 109–126). Springer. https://doi.org/10.1007/978-3-031-35949-1_8
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Publisher DOI: 
10.1007/978-3-031-35949-1_8
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Publication Type: 
Inproceedings - Full-Paper Contribution
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Language: 
English
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Authors: 
Behrisch, Mike 
Renkin, Leon 
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Organisational Unit: 
E104-01 - Forschungsbereich Algebra 
E104 - Institut für Diskrete Mathematik und Geometrie 
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Published in: 
Formal Concept Analysis: 17th International Conference, ICFCA 2023, Kassel, Germany, July 17–21, 2023, Proceedings 
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ISBN: 
978-3-031-35949-1
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Volume: 
13934
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DOI of the book: 
10.1007/978-3-031-35949-1
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Date (published): 
6-Jul-2023
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Event name: 
17th International Conference on Formal Concept Analysis (ICFCA 2023) 
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Event date: 
17-Jul-2023 - 21-Jul-2023
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Event place: 
Kassel, Germany
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Number of Pages: 
18
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Publisher: 
Springer, Cham
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Peer reviewed: 
Yes
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Keywords: 
centralising monoid; witness; context reduction
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Abstract: 
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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Project (external): 
FWF
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Project ID: 
P 33878
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Link (external): 
https://doi.org/10.5281/zenodo.7641814
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Research Areas: 
Logic and Computation: 35%
Fundamental Mathematics Research: 65%
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Science Branch: 
1020 - Informatik: 35%
1010 - Mathematik: 65%
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Appears in Collections:
Conference Paper

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