The Alon–Jaeger–Tarsi conjecture via group ring identities
In this paper we resolve the Alon–Jaeger–Tarsi conjecture (dating back to 1981) for sufficiently large primes. Namely, we show that for any finite field \mathbb{F} of size 61<|\mathbb{F}|\ne 79 and any nonsingular matrix M over \mathbb{F} there exists a vector x such that neither x nor Mx has a zero component.
Authors
- János Nagy
- Péter Pál Pach (ORCID: https://orcid.org/0000-0002-4625-4650)
Institutions
- HUN-REN Alfréd Rényi Institute of Mathematics (HU)
- Budapest University of Technology and Economics (HU)
- Montavid Thermodynamic Research Group (HU)
Publication Details
- Journal
- Journal of the European Mathematical Society
- Published
- 2025-04-11
- DOI
- https://doi.org/10.4171/jems/1640
- Primary Topic
- Advanced Topics in Algebra
- Type
- article
- Field-Weighted Citation Impact
- 0.00