2 citations · 4 across the 29 of their papers we have counts for
32 papers
The Interplay between Additive and Multiplicative Central Sets Theorems
Pintu Debnath, Sayan Goswami, Chunlin Liu
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 Centra…
On dynamical -set and its combinatorial consequences
Pintu Debnath, Sayan Goswami
Using the methods from topological dynamics, H. Furstenberg introduced the notion of a central set and proved the famous Central Sets Theorem. Later D. De, Neil Hindman, and D. Str…
Combined exponential patterns in multiplicative sets
Pintu Debnath, Sayan Goswami
sets play fundamental role in arithmetic Ramsey theory. A set is called an additive set if it is of the form $FS\left(\langle x_{n}\rangle_{n\in \mathbb{N}}\right)=\left\…
On the set of Kronecker numbers
Sayan Goswami, Wen Huang, XiaoSheng Wu
An positive even number is said to be a Kronecker number if it can be written in infinitely many ways as the difference between two primes, and it is believed that all even numbers…
Some remarks on Alweiss's technique and monochromatic configuration of the form over Rationals
Sayan Goswami
In this article, we will explore a recent method of Alweiss \cite{key-1} using ultrafilter technique to study monochromatic partition regular structure of the form $\left\{ x,y,x+y…
An improved threshold for the number of distinct intersections of intersecting families
Jagannath Bhanja, Sayan Goswami
A family of subsets of is called a -intersecting family if for any two members and for some positive i…
A note on distinct differences in -intersecting families
Jagannath Bhanja, Sayan Goswami
For a family of subsets of , let be the collection of all (setwise) differences…
Product of difference sets of set of primes
Sayan Goswami
In a recent work \cite{key-11}, A. Fish proved that if and are two subsets of of positive upper Banach density, then there exists such…
An inductive proof of the Bollobás two family theorem
Sayan Goswami
Inspired by the inductive proof of LYM-inequality given by P. Frankl, we provide an inductive proof of the Bollobás two family theorem.
Additive and multiplicative Gower's Ramsey theorem
Sayan Goswami
W. T. Gower generalized Hindman's Finite sum theorem over by showing that for any finite coloring of $X_{k…
Polynomial extension of the Stronger Central Sets Theorem
Sayan Goswami, Lorenzo Luperi Baglini, Sourav Kanti Patra
In [F81] Furstenberg introduced the notion of central set and established his famous Central Sets Theorem. Since then, several improved versions of Furstenberg's result have been f…
An infinitary Zero sum theorem
Sayan Goswami
Erdős-Ginzburg-Ziv theorem says that if there are 2n-1 number is given, then there are n numbers such that their sum is divided by n. We will connect this theorem with the Ramsey t…
Nonstandard proof of combined sum and product structure in IP sets
Sayan Goswami
V. Bergelson and N. Hindman proved that sets contain all possible finite sum and product of a sum subsystem of any sequence in . In this article, we will prove…
Dynamical IP-sets in weak rings
Pintu Debnath, Sayan Goswami
V. Bergelson and N. Hindman proved that IP- sets contain all possible finite sums and products of a sum subsystem of any sequence in . In a recent work the se…
Elementary characterization of essential F-sets and its combinatorial consequences
Dibyendu De, Pintu Debnath, Sayan Goswami
There is a long history of studying Ramsey theory using the algebraic structure of the Stone-Čech compactification of discrete semigroup. It has been shown that various Ramsey theo…
Some new symmetric structures in Ramsey theory
Aninda Chakraborty, Sayan Goswami
In this article, we will investigate several new configurations in Ramsey Theory, using the $\ostar_{l,k}$-operation on the set of integers, recently introduced in \cite{key-4}. Th…
Dynamical characterization of central sets along filter
Pintu Debnath, Sayan Goswami
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…
Central Sets Theorem along filters and some combinatorial consequences
Sayan Goswami, Jyotirmoy Poddar
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 the…
An abstract formulation of image partition regularity
Aninda Chakraborty, Sayan Goswami
Inspired by the paper [1] of V. Bergelson, John H.Johnson Jr., J. Moreira, we formulate an abstract version of image partition regularity. To establish the result we have used a va…
An analogue to infinitery Hales-Jewett theorem
Aninda Chakraborty, Sayan Goswami
In a recent work, N. Hindman, D. Strauss and L. Zamboni have shown that the Hales-Jewett theorem can be combined with a sufficiently well behaved homomorphisms. In this paper we wi…
Hales-Jewett type configurations in small sets
Aninda Chakraborty, Sayan Goswami
In a recent work, N. Hindman, D. Strauss and L. Zamboni have shown that the Hales-Jewett theorem can be combined with a sufficiently well behaved homomorphisms. Their work was comp…
A combinatorial viewpoint on preserving notion of largeness and an abstract Rado theorem
Sayan Goswami, Subhajit Jana
In this paper we will systematically study the preservation of the notion of largeness of sets, arises from the algebraic structure of Stone-Cech compactification, under homomorphi…
Essential F sets and mixing properties
Pintu Debnath, Sayan Goswami
There is a long history of studying Ramsey theory using the algebraic structure of Stone-Cech compactification of discrete semigroup. It has been shown that various Ramsey theoreti…
A combinatorial approach to central to theorem
Sayan Goswami
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 s…