A virtually nilpotent group with non D-finite Green series

Autor:	Bodart, Corentin
Rok vydání:	2024
Předmět:	Mathematics - Group Theory Mathematics - Combinatorics Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	We provide an example of a virtually $2$-step nilpotent group, and a specific generating set, for which the Green series (sometimes called cogrowth series) is not D-finite. The proof relies on an arithmetical miracle, and the study of the subword complexity of a multiplicative sequence coming out of it. Comment: 11 pages, 2 figures. Comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.13395 Zobrazit plný text záznamu View this record from Arxiv