在Dyer-Lashof代数和$H_*QS^0$中寻找$\mathcal{A}$ -湮没类的算法I.适用于低长度和低尺寸表的闭合形式
An algorithmic search for $\mathcal{A}$-annihilated classes in the Dyer-Lashof algebra and $H_*QS^0$ I. Closed form for low lengths and tables in low dimensions
摘要：
这项工作的目的是公布一些计算结果，涉及表包含$\mathcal{A}$ -歼灭单项式，不包括方类，在戴尔-Lashof代数和$H_*QS^0$ ;我们的计算到维度$1.1\times 10^7$，但在本文中的表只宣布结果到维度$2^{17}=131072$和完整的表将根据要求提供。我们计算的理论背景是由Curtis \cite{Curtis}和Wellington \cite{Wellington}关于Dyer-Lashof代数的$\mathcal{A}$ -模结构以及$H_*QS^0$的工作提供的。在我们看来，有一个可行的算法来做这些计算，我们计划在未来的工作中宣布，部分是为了避免使这篇论文比它长。我们希望收到专家对这些计算的反馈，并尽快提供我们的算法。我们希望这些表为该领域的研究人员提供一个来源，以及一个数据库来分析这些序列的行为，它们的分布和其他渐近行为。在$H_*QS^0$中计算球形类的问题以及对称和非对称命中问题一直是我们追求这个项目的主要动机。
英文摘要：
The aim of this work is to publicise some computational results involving tables which contain $\mathcal{A}$-annihilated monomials, excluding square classes, in the Dyer-Lashof algebra and $H_*QS^0$; our computations go up to dimension $1.1\times 10^7$ but the tables in this paper only announce results up to dimension $2^{17}=131072$ and full tables would be available upon request. The theoretical background for our computations is provided by work of Curtis \cite{Curtis} and Wellington \cite{Wellington} on the $\mathcal{A}$-module structure of the Dyer-Lashof algebra as well as $H_*QS^0$. It seems to us that there is a workable algorithm to do these computations which we plan to announce in a future work, partly to avoid making this paper longer than it is. We hope to receive feedback from the experts on these computations and make our algorithm available as soon as we can. We hope that these tables provide a source for researchers in the field, as well as a pool of data to analyse the behaviour of these sequences, their distributions and other asymptotic behaviours. The problem of computing spherical classes in $H_*QS^0$ as well as the symmetric and non-symmetric hit problems have been our main motivations to pursue this project.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
