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arXiv · 2409.13395

A virtually nilpotent group whose Green series is not D-finite

Corentin Bodart
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Abstract

We provide the first example of virtually nilpotent group, with 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.

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Corentin Bodart. 2024-09-20. A virtually nilpotent group whose Green series is not D-finite. https://doi.org/10.1142/s0218196726500074

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