关系的轮廓
The Profile of relations
摘要：
关系结构$R$的{ \it profile}是函数$ϕ_R$，它对每个整数$n$计数直到同构的它的$n$元素子结构的数目。许多计数函数都是配置文件。有趣的例子来自置换群。一些突出的事实的行为的配置文件。从有序集和组合学（特别是良好的准序的概念，有序代数的相关概念，拉姆齐定理）的技术进行了说明。正在进行的研究建议将关系结构$R$的轮廓看作与$R$相关的某个分次代数的Hilbert函数。给出了P. J. Cameron关于轨道代数环的完整性的一个猜想的解的一个暗示。本文介绍了Y.Boudabbous和N.Thiéry关于若轮廓的增长是多项式的（且结构具有有限核）则轮廓是拟多项式的猜想的最新进展。
英文摘要：
The {\it profile} of a relational structure $R$ is the function $ϕ_R$ which counts for every integer $n$ the number of its $n$-element substructures up to an isomorphism. Many counting functions are profiles. Interesting examples come from permutation groups. Some salient facts about the behavior of the profile are presented. Techniques from ordered sets and combinatorics (notably the notion of well-quasi-order, the related notions of ordered algebras, Ramsey theorem) are illustrated. Ongoing resarch suggests to view the profile of a relational structure $R$ as the Hilbert function of some graded algebra associated with $R$. A hint at the solution of a conjecture of P.J.Cameron on the integrity of the ring of the orbit algebra is given. Recent progress made with Y.Boudabbous and N.Thiéry on the conjecture that the profile is a quasi-polynomial if its growth is polynomial (and the structure has a finite kernel) are presented.
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