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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.02629 |
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| _version_ | 1866913690032275456 |
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| author | Pramanick, Anik Saikh, MD Mursalim |
| author_facet | Pramanick, Anik Saikh, MD Mursalim |
| contents | The Central sets theorem was first introduced by H. Furstenberg
[F] in terms of Dynamical systems. Later Hindman and Bergelson extended
the theorem using Stone-$Č$ech compactification $β$$\mathbb{N}$ of $\mathbb{N}$. In [SY] algebraic
characterization of Central sets was done for semigroup and equivalence of
Dynamical and Algebraic characterizations were shown. D. De, N. Hindman,
and D. Strauss proved a stronger version of the Central sets theorem for semigroup. D. Phulara generalized that theorem for commutative semigroup taking
a sequence of Central sets. Recently J. Podder and S. Pal established the
Phulara type generalization of Central sets theorem near zero [PP]. We did
this for arbitrary adequate partial semigroup and VIP systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02629 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized central sets theorem for partial semigroups and vip systems Pramanick, Anik Saikh, MD Mursalim Combinatorics The Central sets theorem was first introduced by H. Furstenberg [F] in terms of Dynamical systems. Later Hindman and Bergelson extended the theorem using Stone-$Č$ech compactification $β$$\mathbb{N}$ of $\mathbb{N}$. In [SY] algebraic characterization of Central sets was done for semigroup and equivalence of Dynamical and Algebraic characterizations were shown. D. De, N. Hindman, and D. Strauss proved a stronger version of the Central sets theorem for semigroup. D. Phulara generalized that theorem for commutative semigroup taking a sequence of Central sets. Recently J. Podder and S. Pal established the Phulara type generalization of Central sets theorem near zero [PP]. We did this for arbitrary adequate partial semigroup and VIP systems. |
| title | Generalized central sets theorem for partial semigroups and vip systems |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.02629 |