A combinatorial approach to exponential patterns in multiplicative $IP^{\star}$ sets in $\mathbb{N}$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913467612528640 |
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| author | Debnath, Pintu |
| author_facet | Debnath, Pintu |
| contents | In [On $IP^{\star}$sets and central sets, Combinatorica, 14 (1994) 269-277], N. Hindman and V.Bergelson proved additive $IP^{\star}$-sets contain finite sums and finite products of a single sequence. An analogous study was made by A. Sisto in [Exponential triples, Electronics Journal of Combinatorics, 18 (2011), no. 147], where he proved that multiplicative $IP^{\star}$-sets contain exponential $IP$ of type $I$ and finite sums of a single sequence as well as exponential $IP$ of type $II$ and finite products of another single sequence,
using the algebra in the Stone-Čech Compactification of discrete semigroups. In this article, we will provide a combinatorial proof of the result of A. Sisto. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A combinatorial approach to exponential patterns in multiplicative $IP^{\star}$ sets in $\mathbb{N}$ Debnath, Pintu Combinatorics 05D10, 22A15, 54D35 In [On $IP^{\star}$sets and central sets, Combinatorica, 14 (1994) 269-277], N. Hindman and V.Bergelson proved additive $IP^{\star}$-sets contain finite sums and finite products of a single sequence. An analogous study was made by A. Sisto in [Exponential triples, Electronics Journal of Combinatorics, 18 (2011), no. 147], where he proved that multiplicative $IP^{\star}$-sets contain exponential $IP$ of type $I$ and finite sums of a single sequence as well as exponential $IP$ of type $II$ and finite products of another single sequence, using the algebra in the Stone-Čech Compactification of discrete semigroups. In this article, we will provide a combinatorial proof of the result of A. Sisto. |
| title | A combinatorial approach to exponential patterns in multiplicative $IP^{\star}$ sets in $\mathbb{N}$ |
| topic | Combinatorics 05D10, 22A15, 54D35 |
| url | https://arxiv.org/abs/2403.09585 |