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arXiv · 2605.19542

Linear Algebraic Method and the Erd\H{o}s-Heilbronn Conjecture

Guanzhong Yang
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Abstract

Additive combinatorics asks for lower bounds on sumsets and restricted sumsets over finite fields. Central examples are the Cauchy-Davenport theorem and the Erd\H{o}s-Heilbronn conjecture. In this note, we develop Das's linear algebraic method and give a new elementary proof of the Alon-Nathanson-Ruzsa theorem for restricted sumsets, which implies the Erd\H{o}s-Heilbronn conjecture. Compared with the classical polynomial method via Combinatorial Nullstellensatz, our proof uses only basic linear algebra over finite fields, including Vandermonde matrices and solvability of linear systems.

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Guanzhong Yang. 2026-05-19. Linear Algebraic Method and the Erd\H{o}s-Heilbronn Conjecture. https://arxiv.org/abs/2605.19542

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