A253948 Number of finite, negative, Archimedean, commutative, totally ordered monoids of size n (semi-groups with a neutral element that is also the top element).

1, 1, 1, 2, 6, 22, 95, 471, 2670, 17387, 131753, 1184059, 12896589

Offset: 1

Author

Milan Petrík, Jan 20 2015

Keywords

• nonn
• hard
• more

Comments

Also number of Archimedean triangular norms on an n-chain.

The terms have been computed using the algorithm described in the referenced papers.

Links

• M. Petrík, GitLab repository with an implementation of the algorithm in Python 3
• M. Petrík, Many-Valued Conjunctions. Habilitation thesis, Czech Technical University in Prague, Faculty of Electrical Engineering, Prague, Czech Republic. Submitted in 2020. Available at Czech Technical University Digital Library.
• M. Petrík and Th. Vetterlein, Rees coextensions of finite tomonoids and free pomonoids. Semigroup Forum 99 (2019) 345-367. DOI: 10.1007/s00233-018-9972-z.
• M. Petrík and Th. Vetterlein, Rees coextensions of finite, negative tomonoids. Journal of Logic and Computation 27 (2017) 337-356. DOI: 10.1093/logcom/exv047.
• M. Petrík and Th. Vetterlein, Algorithm to generate finite negative totally ordered monoids. In: IPMU 2016: 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Eindhoven, Netherlands, June 20-24, 2016.
• M. Petrík and Th. Vetterlein, Algorithm to generate the Archimedean, finite, negative tomonoids. In: Joint 7th International Conference on Soft Computing and Intelligent Systems and 15th International Symposium on Advanced Intelligent Systems. Kitakyushu, Japan, Dec. 3-6, 2014. DOI: 10.1109/SCIS-ISIS.2014.7044822.
• Index entries for sequences related to monoids

Crossrefs

Cf. A058129, A030453, A253949, A253950.

Extensions

a(13) from Milan Petrík, May 09 2021