The Alon–Jaeger–Tarsi conjecture via group ring identities
Year: 2025
Type: article
Abstract: 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.
DOI: 10.4171/jems/1640
Authors: János Nagy, Péter Pál Pach
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409364970