装饰集团的操作I：建筑和装饰
Operads of decorated cliques I: Construction and quotients
摘要：
我们引入了一个函子构造$\mathsf{C}$，它以酉岩浆$\mathcal{M}$为输入，并产生操作数。所得到的操作涉及由$\mathcal{M}$的元素标记的和弦的配置，称为$\mathcal{M}$ -装饰集团和一般的和弦配置。通过考虑定义的$\mathcal{M}$ -装饰团的组合子族，例如，通过限制交叉对角线的最大数目或顶点的最大度，我们得到了$\mathsf{C} \mathcal{M}$的子运算域和子代数.这导致了一个新的层次结构的操作，其中包括操作的非交叉配置，Motzkin配置，森林，解剖的多边形，和对合。此外，结构$\mathsf{C}$导致单和双重多重波浪符的操作数和重力操作数的替代定义。
英文摘要：
We introduce a functorial construction $\mathsf{C}$ which takes unitary magmas $\mathcal{M}$ as input and produces operads. The obtained operads involve configurations of chords labeled by elements of $\mathcal{M}$, called $\mathcal{M}$-decorated cliques and generalizing usual configurations of chords. By considering combinatorial subfamilies of $\mathcal{M}$-decorated cliques defined, for instance, by limiting the maximal number of crossing diagonals or the maximal degree of the vertices, we obtain suboperads and quotients of $\mathsf{C} \mathcal{M}$. This leads to a new hierarchy of operads containing, among others, operads on noncrossing configurations, Motzkin configurations, forests, dissections of polygons, and involutions. Besides, the construction $\mathsf{C}$ leads to alternative definitions of the operads of simple and double multi-tildes, and of the gravity operad.
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