Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 2, pp. 537-555 (2000)

Pairwise Intersections of Slupecki Type Maximal Partial Clones

Lucien Haddad, Dietlinde Lau

Département de Mathématiques et d'Informatique, College militaire royal du Canada, boite postale 17000, STN Forces, Kingston ON K7K 7B4 Canada; Fachbereich Mathematik, Universität Rostock, Universitätsplatz 1, 18055 Rostock, Germany, e-mail:

Abstract: Let $k \ge 2$ and $ k$ be a $k$-element set. We study the pairwise intersections of all maximal partial clones of Slupecki type on $ k$. More precisely, we show that with one exception, if $M$ and $M'$ are two strong maximal partial clones of Slupecki type on $ k$, then $M \cap M'$ is covered by both $M$ and $M'$. We also show that the situation is quite different if the non-strong maximal partial clone on $ k$ is involved in the intersection.

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