论文标题
关于有限$ l $ - 代数的枚举
On the enumeration of finite $L$-algebras
论文作者
论文摘要
我们使用约束满意度方法来构建和枚举有限的$ l $代数，以达到同构。这些对象最近是由Rump引入的，并出现在Garside理论，代数逻辑以及组合Yang-Baxter方程的研究中。有37732225 $ L $ - 代数的同构类别为8八。构建的数据库表明，某些类别的$ l $代数和众所周知的组合对象之间存在着两种徒的射击。一方面，我们证明了有限线性$ l $ - 代数的同构类别的钟数。另一方面，我们还证明有限的常规$ l $代数与无限维幼年图相对应。
We use Constraint Satisfaction Methods to construct and enumerate finite $L$-algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the combinatorial Yang-Baxter equation. There are 377322225 isomorphism classes of $L$-algebras of size eight. The database constructed suggest the existence of bijections between certain classes of $L$-algebras and well-known combinatorial objects. On the one hand, we prove that Bell numbers enumerate isomorphism classes of finite linear $L$-algebras. On the other hand, we also prove that finite regular $L$-algebras are in bijective correspondence with infinite-dimensional Young diagrams.
