论文标题
关于伯里斯·威拉德猜想的笔记
A note on the Burris-Willard conjecture
论文作者
论文摘要
根据Daniľčenko的结果，1987年Burris和Willard猜想，在任何$ k $ element域中，$ k \ geq 3 $都可以从其$ k $ - y-ary零件中生成每个centeriasiser克隆。后来，对于每$ k \ geq 3 $，雪地构造的代数构建，带有$ k $ element载体套件，其中可以从中产生的术语操作的最低含量，至少可以从中产生$（k-1）^2 $，该元素比$ k $ k $ k $ k $ k \ geq 3 $。 我们证明，雪的例子并不违反伯里斯·威拉德的猜想，也不违反daniľčenko的结果无效，后者所基于的。我们还为结果补充了一些计算证据，以$ k = 3 $，由算法获得，以计算有限生成的关系克隆在有限集的有限生成的关系克隆中的关系。
Based on results by Daniľčenko, in 1987 Burris and Willard have conjectured that on any $k$-element domain where $k\geq 3$ it is possible to bicentrically generate every centraliser clone from its $k$-ary part. Later, for every $k\geq 3$, Snow constructed algebras with a $k$-element carrier set where the minimum arity of the clone of term operations from which the bicentraliser can be generated is at least $(k-1)^2$, which is larger than $k$ for $k\geq 3$. We prove that Snow's examples do not violate the Burris-Willard conjecture nor invalidate the results by Daniľčenko on which the latter is based. We also complement our results with some computational evidence for $k=3$, obtained by an algorithm to compute a primitive positive definition for a relation in a finitely generated relational clone over a finite set.
