PreprintCC BY 4.0arXiv
Brauer-Kuroda relations for ramified graph covers
Abstract
We establish graph-theoretic analogues of the Brauer-Kuroda relations for ramified Galois covers of finite graphs with arbitrary finite Galois groups. These formulas relate the numbers of spanning trees of intermediate quotient graphs and recover the corresponding formulas for unramified covers. Our proofs use h-functions defined on multiplicity spaces of complex representations of the Galois group.
Related
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BibTeX
@misc{mizuno2026brauerkuroda,
title = {{Brauer-Kuroda relations for ramified graph covers}},
author = {Kosuke Mizuno},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25111},
eprint = {2609.25111},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25111},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Brauer-Kuroda relations for ramified graph covers
AU - Kosuke Mizuno
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.25111
UR - https://arxiv.org/abs/2609.25111
AB - We establish graph-theoretic analogues of the Brauer-Kuroda relations for ramified Galois covers of finite graphs with arbitrary finite Galois groups. These formulas relate the numbers of spanning trees of intermediate quotient graphs and recover the corresponding formulas for unramified covers. Our proofs use h-functions defined on multiplicity spaces of complex representations of the Galois group.
ER -