Year: 2026
Type: preprint
Abstract: We study digit-appending walks in base $b\geq 2$ along integer linear recurrences with minimal characteristic polynomials having a unique simple dominant root $α$ that lies outside the unit circle. We prove that if $α$ and $b$ are multiplicatively independent, then no infinite walk can have uniformly bounded appended digit lengths. In contrast, we show that when the appended digit length can be unbounded, the same independence hypothesis implies the existence of infinite walks.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222069253