Permutation clones generalise permutation groups and clone theory. We investigate permutation clones defined by relations, or equivalently, the automorphism groups of powers of relations. We find many structural results on the lattice of all relationally defined permutation clones on a finite set. We find all relationally defined permutation clones on two element set. We show that all maximal borrow closed permutation clones are either relationally defined or cancellatively defined. Permutation clones generalise clones to permutations of $A^n$. Emil Je\v{r}\'{a}bek found the dual structure to be weight mappings $A^k\rightarrow M$ to a commutative monoid, generalising relations. We investigate the case when the dual object is precisely a relation, equivalently, that $M={\mathbb B}$, calling these relationally defined permutation clones. We determine the number of relationally defined permutation clones on two elements (13). We note that many infinite classes of clones collapse when looked at as permutation clones.

翻译：置换克隆是置换群与克隆理论的推广。本文研究由关系定义的置换克隆，等价地，即关系幂的自同构群。我们在有限集上获得了关于所有关系定义置换克隆格的诸多结构性质。我们完整刻画了二元集上所有关系定义的置换克隆。我们证明所有极大借位封闭置换克隆要么是关系定义的，要么是消去定义的。置换克隆将克隆推广为$A^n$上的置换。Emil Jeřábek发现其对偶结构是到交换幺半群的权重映射$A^k\rightarrow M$，这是对关系的推广。我们研究对偶对象恰好为关系的情形（等价地，即$M={\mathbb B}$），称此类为关系定义置换克隆。我们确定了二元集上关系定义置换克隆的数量（13个）。我们指出，当作为置换克隆考察时，许多无限克隆类会发生坍缩。