Monochromatic polynomial sumset structures on $\mathbb{N}$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917208205033472 |
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| author | Lian, Zhengxing Xiao, Rongzhong |
| author_facet | Lian, Zhengxing Xiao, Rongzhong |
| contents | In the paper, we search for monochromatic infinite additive structures involving polynomials over $\mathbb{N}$. It is proved that for any $r\in \mathbb{N}$, any two distinct natural numbers $a,b$, and any $2$-coloring of $\mathbb{N}$, there exist two sets $B,C\subset \mathbb{N}$ with $|B|=r$ and $|C|=\infty$ such that there exists some color containing $B+aC$ and $B+bC$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monochromatic polynomial sumset structures on $\mathbb{N}$ Lian, Zhengxing Xiao, Rongzhong Combinatorics Dynamical Systems Number Theory In the paper, we search for monochromatic infinite additive structures involving polynomials over $\mathbb{N}$. It is proved that for any $r\in \mathbb{N}$, any two distinct natural numbers $a,b$, and any $2$-coloring of $\mathbb{N}$, there exist two sets $B,C\subset \mathbb{N}$ with $|B|=r$ and $|C|=\infty$ such that there exists some color containing $B+aC$ and $B+bC$. |
| title | Monochromatic polynomial sumset structures on $\mathbb{N}$ |
| topic | Combinatorics Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2404.05226 |