We study the indexing systems that correspond to equivariant Steiner and linear isometries operads. When G is a finite abelian group, we prove that a G-indexing system is realized by a Steiner operad if and only if it is generated by cyclic G-orbits. When G is a finite cyclic group, whose order is either a prime power or a product of two distinct primes greater than 3, we prove that a G-indexing system is realized by a linear isometries operad if and only if it satisfies Blumberg and Hill’s horn-filling condition. We also repackage the data in an indexing system as a certain kind of partial order. We call these posets transfer systems, and develop basic tools for computing with them.

中文翻译：

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检测斯坦纳和线性等距操作

我们研究了对应于等变施泰纳和线性等距操作符的索引系统。什么时候G是一个有限阿贝尔群，我们证明G- 索引系统由 Steiner 操作符实现当且仅当它是由循环生成的G-轨道。什么时候G是一个有限循环群，其阶要么是素数的幂，要么是两个大于 3 的不同素数的乘积，我们证明G-分度系统是通过线性等距实现的，当且仅当它满足 Blumberg 和 Hill 的喇叭填充条件时。我们还将索引系统中的数据重新打包为某种偏序。我们将这些 poset 称为传输系统，并开发用于计算的基本工具。