S. Paul

collaborators

4 papers

math.NT2026

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.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.NT2025

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).

Doubly-weighted zero-sum constants

{±1}-weighted zero-sum constants

Qp​-weighted zero-sum constants

An uncountable subring of R with Hausdorff dimension zero

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

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

An uncountable subring of $R$ with Hausdorff dimension zero