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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2605.19542 |
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| _version_ | 1866917510957236224 |
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| author | Yang, Guanzhong |
| author_facet | Yang, Guanzhong |
| contents | Additive combinatorics asks for lower bounds on sumsets and restricted sumsets over finite fields. Central examples are the Cauchy-Davenport theorem and the Erdős-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 Erdős-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19542 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear Algebraic Method and the Erdős-Heilbronn Conjecture Yang, Guanzhong Combinatorics Rings and Algebras 11B75 (Primary), 11P70 (Secondary), 15A03 (Secondary) Additive combinatorics asks for lower bounds on sumsets and restricted sumsets over finite fields. Central examples are the Cauchy-Davenport theorem and the Erdős-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 Erdős-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. |
| title | Linear Algebraic Method and the Erdős-Heilbronn Conjecture |
| topic | Combinatorics Rings and Algebras 11B75 (Primary), 11P70 (Secondary), 15A03 (Secondary) |
| url | https://arxiv.org/abs/2605.19542 |