Some negative answers to the Bergelson-Hindman's question
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866908450115551232 |
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| author | Wu, Qinqi |
| author_facet | Wu, Qinqi |
| contents | Let $p_1,\dots,p_d$ be integral polynomials vanishing at $0$. It was asked by Bergelson and Hindman whenever $A$ is large, whether the set $\{(m,n)\in \mathbb{N}^2:m+p_1(n),m+p_2(n),\dots,m+p_d(n)\in A\}$ be large in the same sense. In this paper, we give negative answers to this question when ``large'' being the notions of ``central*'', ``IP*'', ``IP$_n$*'', ``IP$_{<ω}$*'' and ``$Δ$*''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03447 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some negative answers to the Bergelson-Hindman's question Wu, Qinqi Combinatorics Let $p_1,\dots,p_d$ be integral polynomials vanishing at $0$. It was asked by Bergelson and Hindman whenever $A$ is large, whether the set $\{(m,n)\in \mathbb{N}^2:m+p_1(n),m+p_2(n),\dots,m+p_d(n)\in A\}$ be large in the same sense. In this paper, we give negative answers to this question when ``large'' being the notions of ``central*'', ``IP*'', ``IP$_n$*'', ``IP$_{<ω}$*'' and ``$Δ$*''. |
| title | Some negative answers to the Bergelson-Hindman's question |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.03447 |