论文标题
Bose-Mesner代数和涂鸦关联方案的功能性
Functoriality of Bose-Mesner algebras and profinite association schemes
论文作者
论文摘要
我们表明，将通勤关联方案的一组原始愿望是来自交换缔合方案类别的函数，这些方案具有溢流性形态的类别，即具有溢流性部分函数的有限集合类别。然后，我们考虑由溢流（我们称为Profinite关联方案）组成的交换结合方案的投影系统，为此定义了Bose-Mesner代数，并描述了此类方案的Delsarte理论。这是将关联方案推广到无限集的另一种方法，与Barg和Skriganov的方法有关。研究了与$（t，m，s）$ - 网和$（t，s）$ - 序列的关系。从这个角度来看，我们谴责了马丁·斯汀森的一些结果。
We show that taking the set of primitive idempotents of commutative association schemes is a functor from the category of commutative association schemes with surjective morphisms to the category of finite sets with surjective partial functions. We then consider projective systems of commutative association schemes consisting of surjections (which we call profinite association schemes), for which Bose-Mesner algebra is defined, and describe a Delsarte theory on such schemes. This is another method for generalizing association schemes to those on infinite sets, related with the approach by Barg and Skriganov. Relation with $(t,m,s)$-nets and $(t,s)$-sequences is studied. We reprove some of the results of Martin-Stinson from this viewpoint.
