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A354497
Number of strictly left-sided quantales on n elements, up to isomorphism. Also number of strictly right-sided quantales on n elements, up to isomorphism.
1
1, 1, 4, 23, 164, 1482, 15838, 197262, 2830649
OFFSET
1,3
COMMENTS
For definition of quantale see A354493.
A quantale is strictly left-sided if every element x satisfies T * x = x, and strictly right-sided if every element x satisfies x * T = x. Here T denotes the top element of the underlying lattice.
Transposition of the semigroup table yields a bijection between strictly left-sided and strictly right-sided quantales, so this sequence counts either type.
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.
CROSSREFS
Sequence in context: A342988 A304074 A307402 * A111547 A171992 A158884
KEYWORD
nonn,more
AUTHOR
Arman Shamsgovara, Aug 03 2022
STATUS
approved