论文标题
几乎是阿贝尔群体的方程式：语言和成长
Equations in virtually abelian groups: languages and growth
论文作者
论文摘要
本文探讨了几乎阿伯利亚群体中方程系统的解决方案集合的性质。我们从两个角度查看这个问题。从正式的语言角度来看，我们证明了方程式系统的解决方案集成了一种自然正常形式的EDT0L语言。从增长来看，我们表明解决方案语言的增长系列是理性的。此外，将一组解决方案作为组元素的一组，我们表明它与任何有限生成集具有合理的相对增长序列。
This paper explores the nature of the solution sets of systems of equations in virtually abelian groups. We view this question from two angles. From a formal language perspective, we prove that the set of solutions to a system of equations forms an EDT0L language, with respect to a natural normal form. Looking at growth, we show that the growth series of the language of solutions is rational. Furthermore, considering the set of solutions as a set of tuples of group elements, we show that it has rational relative growth series with respect to any finite generating set.
