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The Alon–Jaeger–Tarsi conjecture via group ring identities

  • János Nagy

    Budapest University of Technology and Economics, Budapest, Hungary; MTA-BME Lendület “Momentum” Arithmetic Combinatorics Research Group, Budapest, Hungary

  • Péter Pál Pach

    HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary; MTA–HUN-REN RI Lendület “Momentum” Arithmetic Combinatorics Research Group, Budapest, Hungary; Budapest University of Technology and Economics, Budapest, Hungary
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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 of size and any nonsingular matrix over there exists a vector such that neither nor has a zero component.

Cite this article

János Nagy, Péter Pál Pach, The Alon–Jaeger–Tarsi conjecture via group ring identities. J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1640