用解析组合学枚举化学结构、立体异构体和立体单元
Enumerating Chemical Structures, Stereoisomers, and Stereogenic Units with Analytic Combinatorics
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中文总结 AI 辅助
本研究将解析组合学框架应用于化学结构等枚举问题，利用符号法简化了烃类等经典计数，扩展到含立体异构的复杂分子，且通过CombOL软件实现结果可复现。
中文摘要 AI 辅助
传统化学结构枚举依赖图论和群论技术（包括波利亚理论）来处理立体化学对称性，这些方法需要针对每个感兴趣的分子家族进行定制推导，对于非平凡类别的分子很快会变得非常复杂。本研究证明解析组合学提供了一个统一、高度可扩展且相对简单的枚举问题框架。利用符号法，我们表明经典计数问题（如无环烷烃和其他烃类家族的枚举）可通过目标类别的简洁组合规范自然解决。我们首先通过在该框架内复现现有结果来展示此方法的简洁性，所需工作量远少于以往，随后将这些思路扩展到更复杂的问题：计数更广泛的分子类别（同时考虑四面体和E/Z立体异构）、统计立体单元的分布，以及枚举非手性和内消旋化合物。所有结果均可通过开源软件包CombOL实现可复现，该软件可自动将组合规范转换为生成函数（采用符号法），并执行单变量和多变量枚举。
英文摘要
The enumeration of chemical structures traditionally relies on graph- and group-theoretic techniques, including Pólya theory, in order to account for stereochemical symmetries. These methods require bespoke derivations and methods for each molecular family of interest, and quickly become very intricate for nontrivial classes. In this work, we demonstrate that analytic combinatorics provides a unifying, highly extensible, and relatively simple framework for enumeration problems. Using the symbolic method, we show that classical counting problems, such as the enumeration of acyclic alkanes and other hydrocarbon families, can be naturally solved via concise combinatorial specifications of the class of interest. We first demonstrate the simplicity of this approach by replicating existing results in this framework, requiring significantly less work than previously necessary, and then extend these ideas to more complex problems, counting broader classes of molecules accounting for both tetrahedral and E/Z stereoisomerism, counting the distribution of stereogenic units, and enumerating achiral and meso compounds. All results are made reproducible through CombOL, our open-source software package which automates the translation of combinatorial specifications into generating functions using the symbolic method, and performs both univariate and multivariate enumeration.
发表机构
- University of Southern Denmark（南丹麦大学）
- Bielefeld University（比勒费尔德大学）
机构由 AI 辅助整理，请以论文原文为准。
