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Furstenberg introduced the notion of Central sets in 1981. Later in 1990 V. Bergelson and N. Hindman proved a different but an equivalent version of the central set theorem. In 2008 D. De, N. Hindman and D. Strauss proved a stronger version…

H. Furstenberg introduced the notion of central sets in terms of topological dynamics and established the famous Central Sets Theorem. Later in [A new and stronger Central Sets Theorem, Fund. Math. 199 (2008), 155-175], D. De, N. Hindman,…

Using dynamics, Furstenberg defined the concept of a central subset of positive integers and proved several powerful combinatorial properties of central sets. Later using the algebraic structure of the Stone-\v{C}ech compactification,…

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-$\v{C}$ech compactification $\beta$$\mathbb{N}$ of $\mathbb{N}$. In [SY]…

The concept of Central sets, introduced by Furstenberg through the framework of topological dynamics, has played a pivotal role in combinatorial number theory. Furstenberg's Central Sets Theorem highlighted their rich combinatorial…

Hindman's theorem and van der Waerden's theorem are two classical Ramsey theoretic results, the first one deals with finite configurations and the second one deals with infinite configurations. The Central Sets Theorem due to Furstenberg is…

We establish and fully characterize the multidimensional extension of the Stronger Central Sets Theorem. Additionally, we develop a polynomial generalization of this result. Our approach utilizes tools from the Algebra of the Stone-\v{C}ech…

The Central Sets Theorem, a fundamental result in Ramsey theory, is a joint extension of both Hindman's theorem and van der Waerden's theorem. It was originally introduced by H. Furstenberg using methods from topological dynamics. Later,…

The Central Sets Theorem was introduced by H. Furstenberg and then afterwards several mathematicians have provided various versions and extensions of this theorem. All of these theorems deal with central sets, and its origin from the…

The most powerful formulation of the Central Sets Theorem in an arbitrary semigroup was proved in the work of De, Hindman, and Strauss. The sets which satisfy the conclusion of the above Central Sets Theorem are called $C$-sets. The…

H. Furstenberg introduced the notion of central set in terms of topological dynamics and established the central set theorem. The essence of central set theorem is that it is the simultaneous extension of van der Waerden's theorem and…

In \cite[Proposition 8.21 Page-169]{F} Using the methods of topological dynamics, H. Furstenberg introduced the notion of central set and proved the famous Central Sets Theorem. Later, in \cite{DHS}, D. De, H. Hindman and D. Struss…

Using the notions of Topological dynamics, H. Furstenberg defined central sets and proved the Central Sets Theorem. Later V. Bergelson and N. Hindman characterized central sets in terms of algebra of the Stone-\v{C}ech compactification of…

Furstenberg, using tools from topological dynamics, defined the notion of a central subset of positive integers, and proved a powerful combinatorial theorem about such sets. Using the algebraic structure of the Stone-\v{C}ech…

Using the methods from topological dynamics, H. Furstenberg introduced the notions of Central sets and proved the famous Central Sets Theorem which is the simultaneous extension of the van der Waerden and Hindman Theorem. Later N. Hindman…

In the 1970s Deuber introduced the notion of $(m,p,c)$-sets in $\mathbb{N}$ and showed that these sets are partition regular and contain all linear partition regular configurations in $\mathbb{N}$. In this paper we obtain enhancements and…

The Central Sets Theorem near zero was originally proved by Hindman and Leader. Later a version of Central Sets Theorem was proved by De, Hindman and Strauss known to be the stronger Central Sets Theorem. Subsequently many other versions of…

N. Hindman and I. Leader introduced the set of ultrafilters 0+ on (0,1) and characterize smallest ideal of (0+,+) and proved the Central Set Theorem near zero. Recently Polynomial Central Set Theorem has been proved by V. Bergelson, J. H.…

In [B] Beiglb\"ock gave a Multidimension Central sets theorem. Recently, [GP] extended this result for polynomials. They proved the Multidimensional Polynomial Central sets theorem. Earlier, Hindman and Leader introduced the near zero…

The Theorems of Hindman and van der Waerden belong to the classical theorems of partition Ramsey Theory. The Central Sets Theorem is a strong simultaneous extension of both theorems that applies to general commutative semigroups. We give a…