论文标题
组合探索：列举算法框架
Combinatorial Exploration: An algorithmic framework for enumeration
论文作者
论文摘要
组合探索是一种新的域 - 不足算法框架，可自动，严格地研究组合对象的结构，并得出其计数序列并生成函数。我们描述了它的工作原理并提供开源Python实现。作为先决条件，我们为组合分解策略和组合规范建立了新的理论基础。 然后，我们将组合探索应用于置换模式的领域，从而产生了很大的影响。我们以统一的方式在文献中进行了数百种结果，并证明了许多新的结果。这些结果可以在https://permpal.com的新的公共数据库，即置换模式避免库（Permpal）中找到。最后，我们提供了三个其他概念证明，展示了组合探索如何证明在交替的符号矩阵，多元和设定分区的域中的结果。
Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequences and generating functions. We describe how it works and provide an open-source Python implementation. As a prerequisite, we build up a new theoretical foundation for combinatorial decomposition strategies and combinatorial specifications. We then apply Combinatorial Exploration to the domain of permutation patterns, to great effect. We rederive hundreds of results in the literature in a uniform manner and prove many new ones. These results can be found in a new public database, the Permutation Pattern Avoidance Library (PermPAL) at https://permpal.com. Finally, we give three additional proofs-of-concept, showing examples of how Combinatorial Exploration can prove results in the domains of alternating sign matrices, polyominoes, and set partitions.
