A357295 Number of balanced quantales on n elements, up to isomorphism.

1, 1, 9, 106, 1597, 29720, 663897, 17747907, 620659554

Offset

1,3

Comments

For definition of quantale see A354493.

A quantale is balanced if T * T = T, where T denotes the top element of the underlying lattice.

References

P. Eklund, J. G. García, U. Höhle, and J. Kortelainen, (2018). Semigroups in complete lattices. In Developments in Mathematics (Vol. 54). Springer Cham.

K. I. Rosenthal, Quantales and their applications. Longman Scientific and Technical, 1990.

Arman Shamsgovara, A catalogue of every quantale of order up to 9 (abstract), LINZ2022, 39th Linz Seminar on Fuzzy Set Theory, Linz, Austria.

Arman Shamsgovara and P. Eklund, A Catalogue of Finite Quantales, GLIOC Notes, December 2019.

Links

Table of n, a(n) for n=1..9.

Crossrefs

Cf. A354493.

Sequence in context: A261428 A122569 A309652 * A367789 A316145 A365032

Adjacent sequences: A357292 A357293 A357294 * A357296 A357297 A357298

Keyword

nonn,more

Author

Arman Shamsgovara, Sep 22 2022

Status

approved