48 citations · 76 across the 23 of their papers we have counts for
24 papers
A concept of largeness of monochromatic sums and products in large ideal domain
Pintu Debnath
An infinite integral domain is called a large ideal domain (LID) if every nontrivial ideal of has finite index in . Recently, N. Hindman and D. Strauss have established…
A combinatorial approach to the stronger Central Sets Theorem for semigroups
Pintu Debnath
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 The…
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…
The finite products of shifted primes and Moreira's Theorem
Pintu Debnath
Let and . Do there exist and such that $\left\{x,y,xy,x+y\right\}\subseteq…
Monocromaticity of additive and multiplicative central sets and Goswami's theorem in large Integral Domains
Pintu Debnath, Sourav Kanti Patra
In \cite{Fi} A. Fish proved that if and are two subsets of of positive upper Banach density, then there exists such that $…