S. Paul

activity

20212026

collaborators

11 papers

math.NT2026

${\pm 1}$ -weighted zero-sum constants

Krishnendu Paul, Shameek Paul

Let $A, B \subseteq Z_{n} ∖ {0}$ . A sequence $S = (x_{1}, \dots, x_{k})$ in $Z_{n}$ is called an $(A, B)$ -weighted zero-sum sequence if there exist $a_{1}, \dots, a_{k} \in A$ …

math.NT2026

$Q_{p}$ -weighted zero-sum constants

Krishnendu Paul, Shameek Paul

A sequence $S = (x_{1}, \dots, x_{k})$ in $Z_{p}$ is called a $(Q_{p}, 1)$ -weighted zero-sum sequence if there exist $a_{1}, \dots, a_{k} \in Q_{p}$ such that $a_{1} x_{1} + \dots + a_{k} x_{k} = 0$ …

math.NT2024

An uncountable subring of $R$ with Hausdorff dimension zero

Stephan Baier, Shameek Paul

We construct a subring as mentioned in the title (hence this subring has Lebesgue measure zero).

math.NT2023

Doubly-weighted zero-sum constants

Krishnendu Paul, Shameek Paul

Let $A, B \subseteq Z_{n}$ be given and $S = (x_{1}, \dots, x_{k})$ be a sequence in $Z_{n}$ . We say that $S$ is an $(A, B)$ -weighted zero-sum sequence if there exist $a_1,\ldots…

math.NT2022

Extremal sequences for the unit-weighted Gao constant of $Z_{n}$

Santanu Mondal, Krishnendu Paul, Shameek Paul

For $A \subseteq Z_{n}$ , the $A$ -weighted Gao constant $E_{A} (n)$ is defined to be the smallest natural number $k$ , such that any sequence of $k$ elements in $Z_{n}$ has a…

math.NT2022

On unit-weighted zero-sum constants of $Z_{n}$

Santanu Mondal, Krishnendu Paul, Shameek Paul

Given $A \subseteq Z_{n}$ , the constant $C_{A} (n)$ is defined to be the smallest natural number $k$ such that any sequence of $k$ elements in $Z_{n}$ has an $A$ -weighted ze…

math.NT2022

Square-weighted zero-sum constants

Krishnendu Paul, Shameek Paul

Let $A \subseteq Z_{n}$ be a subset. A sequence $S = (x_{1}, \dots, x_{k})$ in $Z_{n}$ is said to be an $A$ -weighted zero-sum sequence if there exist $a_{1}, \dots, a_{k} \in A$ such…

math.NT2022

Extremal sequences related to the Jacobi symbol

Santanu Mondal, Krishnendu Paul, Shameek Paul

For a weight-set $A \subseteq Z_{n}$ , the $A$ -weighted zero-sum constant $C_{A} (n)$ is defined to be the smallest natural number $k$ , such that any sequence of $k$ elements in $…

math.NT2021

Zero-sum constants related to the Jacobi symbol

Santanu Mondal, Krishnendu Paul, Shameek Paul

For $A \subseteq Z_{n}$ , the $A$ -weighted Gao constant $E_{A} (n)$ is defined to be the smallest natural number $k$ such that any sequence of $k$ elements in $Z_{n}$ has a s…

math.NT2021

Extremal sequences for a weighted zero-sum constant

Santanu Mondal, Krishnendu Paul, Shameek Paul

The constant $C_{A} (n)$ is defined to be the smallest natural number $k$ such that any sequence of $k$ elements in $Z_{n}$ has a subsequence of consecutive terms whose $A$ -weig…

math.NT2021

On a different weighted zero-sum constant

Santanu Mondal, Krishnendu Paul, Shameek Paul

For a finite abelian group $(G, +)$ , the constant $C (G)$ is defined to be the smallest natural number $k$ such that any sequence in $G$ having length $k$ will have a subsequence of…

{±1}-weighted zero-sum constants

Qp​-weighted zero-sum constants

An uncountable subring of R with Hausdorff dimension zero

Doubly-weighted zero-sum constants

Extremal sequences for the unit-weighted Gao constant of Zn​

On unit-weighted zero-sum constants of Zn​

Square-weighted zero-sum constants

Extremal sequences related to the Jacobi symbol

Zero-sum constants related to the Jacobi symbol

Extremal sequences for a weighted zero-sum constant

On a different weighted zero-sum constant

${\pm 1}$ -weighted zero-sum constants

$Q_{p}$ -weighted zero-sum constants

An uncountable subring of $R$ with Hausdorff dimension zero

Extremal sequences for the unit-weighted Gao constant of $Z_{n}$

On unit-weighted zero-sum constants of $Z_{n}$