S. Paul

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20222026

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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.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…

{±1}-weighted zero-sum constants

Qp​-weighted zero-sum constants

An uncountable subring of R with Hausdorff dimension zero

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

${\pm 1}$ -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 $Z_{n}$