A253948 - OEIS

%I #30 May 28 2021 02:51:26

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

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

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

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

%H M. Petrík, <a href="https://gitlab.com/petrikm/fntom">GitLab repository with an implementation of the algorithm in Python 3</a>

%H M. Petrík, <a href="https://gitlab.com/petrikm/fntom/-/blob/master/papers/Petrik__Habilitation_Thesis.pdf">Many-Valued Conjunctions</a>. Habilitation thesis, Czech Technical University in Prague, Faculty of Electrical Engineering, Prague, Czech Republic. Submitted in 2020. Available at <a href="https://dspace.cvut.cz/handle/10467/91539">Czech Technical University Digital Library</a>.

%H M. Petrík and Th. Vetterlein, <a href="https://gitlab.com/petrikm/fntom/-/blob/master/papers/Petrik_Vetterlein__Pomonoids__preprint.pdf">Rees coextensions of finite tomonoids and free pomonoids</a>. Semigroup Forum 99 (2019) 345-367. DOI: <a href="https://doi.org/10.1007/s00233-018-9972-z">10.1007/s00233-018-9972-z</a>.

%H M. Petrík and Th. Vetterlein, <a href="https://gitlab.com/petrikm/fntom/-/blob/master/papers/Petrik_Vetterlein__Coextensions__preprint.pdf">Rees coextensions of finite, negative tomonoids</a>. Journal of Logic and Computation 27 (2017) 337-356. DOI: <a href="https://doi.org/10.1093/logcom/exv047">10.1093/logcom/exv047</a>.

%H M. Petrík and Th. Vetterlein, <a href="https://gitlab.com/petrikm/fntom/-/blob/master/papers/Petrik_Vetterlein__IPMU_2016__preprint.pdf">Algorithm to generate finite negative totally ordered monoids</a>. In: IPMU 2016: 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Eindhoven, Netherlands, June 20-24, 2016.

%H M. Petrík and Th. Vetterlein, <a href="https://gitlab.com/petrikm/fntom/-/blob/master/papers/Petrik_Vetterlein__SCIS_ISIS_2014__preprint.pdf">Algorithm to generate the Archimedean, finite, negative tomonoids</a>. 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: <a href="https://doi.org/10.1109/SCIS-ISIS.2014.7044822">10.1109/SCIS-ISIS.2014.7044822</a>.

%H <a href="/index/Mo#monoids">Index entries for sequences related to monoids</a>

%Y Cf. A058129, A030453, A253949, A253950.

%K nonn,hard,more

%O 1,4

%A _Milan Petrík_, Jan 20 2015

%E a(13) from _Milan Petrík_, May 09 2021