Equations in virtually abelian groups: Languages and growth

Autor:	Alex Levine, Alex Evetts
Rok vydání:	2022
Předmět:	FOS: Computer and information sciences Formal Languages and Automata Theory (cs.FL) General Mathematics FOS: Mathematics Computer Science - Formal Languages and Automata Theory Group Theory (math.GR) 03D05 20F10 20F65 20K35 68Q45 Mathematics - Group Theory
Zdroj:	International Journal of Algebra and Computation. 32:411-442
ISSN:	1793-6500 0218-1967
Popis:	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. Final version, to appear in Internat. J. Algebra Comput
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df4f6c3baf47d32514da3ccd514238f0 https://doi.org/10.1142/s0218196722500205 Zobrazit plný text záznamu