论文标题
晶格产业和奥尔特德过滤
Lattice operads and operad filtrations
论文作者
论文摘要
我们详细阐述了根据用作索引对象的晶格价值的作战量定义的作战的概念。这涵盖了相关代数的普通整数指数过滤，并作为特殊情况，但该概念似乎很自然，也足以包含其他类型的例子。晶格作业的特性是部分组成相对于与会议和加入的一定分布的特性。我们观察到，一些著名的组合起源晶格家族（例如塔玛里晶格）组装以遵守这种特定特性的作业。其他示例包括在Young的晶格中支持的整数外套，包括$ A，B $和D $的整数组成的作品，我们与我们与常规多台面的经营相关。我们讨论了对称群体上弱顺序与置换术的结构的部分兼容性。
We elaborate on the notion of a filtration of an operad defined in terms of a lattice-valued operad serving as an indexing object. That covers ordinary integer-indexed filtrations of associative algebras and operads as a special case, yet the notion appears to be natural enough to encompass examples of other kind as well. The characteristic property of lattice operads is that of a certain distributivity of partial compositions with respect to meets and joins. We observe that some well-known families of lattices of combinatorial origin, such as Tamari lattices, assemble to operads subject to this particular property. Other examples include an operad of integer paritions supported on Young's lattice, operads of integer compositions of types $A, B$ and $D$, which we relate to operads of regular polytopes. We discuss the partial compatibility of the weak order on the symmetric group with the structure of the permutations operad.
