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

1,4

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

Table of n, a(n) for n=1..13.

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.

Sequence in context: A292096 A006871 A268699 * A248836 A351919 A328500

Adjacent sequences: A253945 A253946 A253947 * A253949 A253950 A253951

Keyword

nonn,hard,more

Author

Milan Petrík, Jan 20 2015

Extensions

a(13) from Milan Petrík, May 09 2021

Status

approved