Sums and differences of sets: a further improvement over AlphaEvolve
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910980418568192 |
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| author | Zheng, Fan |
| author_facet | Zheng, Fan |
| contents | We present a new advancement in the sum and difference of sets problem, which improves upon recent results by both DeepMind's AlphaEvolve ($θ= 1.1584$) and subsequent explicit constructions ($θ= 1.173050$). In this work, we construct a sequence of $U$ sets which in the limit establishes a new lower bound of $θ= 1.173077$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01896 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sums and differences of sets: a further improvement over AlphaEvolve Zheng, Fan Combinatorics Number Theory We present a new advancement in the sum and difference of sets problem, which improves upon recent results by both DeepMind's AlphaEvolve ($θ= 1.1584$) and subsequent explicit constructions ($θ= 1.173050$). In this work, we construct a sequence of $U$ sets which in the limit establishes a new lower bound of $θ= 1.173077$. |
| title | Sums and differences of sets: a further improvement over AlphaEvolve |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2506.01896 |