PreprintCC BY 4.0arXiv
The Bellaterra graphs are Ramanujan
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(√(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.
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BibTeX
@misc{kharlampovich2026bellaterra,
title = {{The Bellaterra graphs are Ramanujan}},
author = {Olga Kharlampovich and Alina Vdovina},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25324},
eprint = {2610.25324},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25324},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Bellaterra graphs are Ramanujan
AU - Olga Kharlampovich
AU - Alina Vdovina
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25324
UR - https://arxiv.org/abs/2610.25324
AB - 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(√(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.
ER -