cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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.

Original entry on oeis.org

1, 1, 4, 23, 164, 1482, 15838, 197262, 2830649
Offset: 1

Views

Author

Arman Shamsgovara, Aug 03 2022

Keywords

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

Cf. A354493, A354496.

A354498 Number of two-sided quantales on n elements, up to isomorphism.

Original entry on oeis.org

1, 2, 8, 47, 354, 3277, 36506, 490983, 8301353
Offset: 1

Views

Author

Arman Shamsgovara, Aug 03 2022

Keywords

Comments

A quantale is two-sided if it is both left- and right-sided. See A354493 for the definition of a quantale and A354496 for the definition of left- and right-sided quantales.

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, to appear), LINZ2022, 39th Linz Seminar on Fuzzy Set Theory, Linz, Austria.

Crossrefs

Cf. A354493, A354496.
Showing 1-2 of 2 results.

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