P. Debnath

activity

20172026

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7 papers · 1 filter

math.DS2024

On dynamical $C^{⋆}$ -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…

math.CO2024

The finite products of shifted primes and Moreira's Theorem

Pintu Debnath

Let $r \in N$ and $N = ⋃_{i = 1}^{r} C_{i}$ . Do there exist $x, y \in N$ and $i \in {1, 2, \dots, r}$ such that $\left\{x,y,xy,x+y\right\}\subseteq…

math.CO2024

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 $E_{1}$ and $E_{2}$ are two subsets of $Z$ of positive upper Banach density, then there exists $k \in Z ∖ 0$ such that $…

math.DS2024

Dynamical characterization of central sets in adequate partial semigroups

Pintu Debnath, Sayan Goswami, Sourav Kanti Patra

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…

math.CO2024

An answer to Goswami's question and new sources of $I P^{⋆}$ -sets containing combined zigzag structure

Pintu Debnath

$A$ set is called $I P$ -set in a semigroup $(S, \cdot)$ if it contains finite products of a sequence. A set that intersects with all $I P$ -sets is called $I P^{⋆}$ -set. I…

math.CO2024

A combinatorial approach to exponential patterns in multiplicative $I P^{⋆}$ sets in $N$

Pintu Debnath

In [On $I P^{⋆}$ sets and central sets, Combinatorica, 14 (1994) 269-277], N. Hindman and V.Bergelson proved additive $I P^{⋆}$ -sets contain finite sums and finite products of…

On dynamical C⋆-set and its combinatorial consequences

The finite products of shifted primes and Moreira's Theorem

Monocromaticity of additive and multiplicative central sets and Goswami's theorem in large Integral Domains

Dynamical characterization of central sets in adequate partial semigroups

An answer to Goswami's question and new sources of IP⋆-sets containing combined zigzag structure

A combinatorial approach to exponential patterns in multiplicative IP⋆ sets in N

On dynamical $C^{⋆}$ -set and its combinatorial consequences

An answer to Goswami's question and new sources of $I P^{⋆}$ -sets containing combined zigzag structure

A combinatorial approach to exponential patterns in multiplicative $I P^{⋆}$ sets in $N$