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%I #7 Sep 11 2022 09:30:58
%S 1,1,4,23,164,1482,15838,197262,2830649
%N 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.
%C For definition of quantale see A354493.
%C 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.
%C Transposition of the semigroup table yields a bijection between strictly left-sided and strictly right-sided quantales, so this sequence counts either type.
%D P. Eklund, J. G. García, U. Höhle, and J. Kortelainen, (2018). Semigroups in complete lattices. In Developments in Mathematics (Vol. 54). Springer Cham.
%D K. I. Rosenthal, Quantales and their applications. Longman Scientific and Technical, 1990.
%D Arman Shamsgovara, A catalogue of every quantale of order up to 9 (abstract), LINZ2022, 39th Linz Seminar on Fuzzy Set Theory, Linz, Austria.
%Y Cf. A354493, A354496.
%K nonn,more
%O 1,3
%A _Arman Shamsgovara_, Aug 03 2022