Year: 2026
Type: preprint
Abstract: The Bellaterra automaton gives three involutions of every set of binary words of a fixed length. We identify their Schreier graph at level $n$ with a cubic arithmetic graph over $\Q(\sqrt{17})$, and prove that every nonconstant adjacency eigenvalue satisfies the Ramanujan bound. In particular, this proves Malyshev-Pak's Conjecture that the Bellaterra graphs form a family of two-sided expanders.
Source: arXiv (Cornell University)
Authors: Kharlampovich, Olga, Vdovina, Alina
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: City University of New York
OpenAlex ID: W7223070197