Arka Ghosh

activity

20242026

collaborators

6 papers

math.AC2026

Powers of Alexander Duals of Stanley-Reisner Ideals of Chessboard Complexes

Arka Ghosh, S. Selvaraja

Let $Δ_{m, n}$ be the chessboard complex, and let $J_{m, n}$ be the Stanley-Reisner ideal of its Alexander dual. We study the symbolic and ordinary powers of $J_{m, n}$ , focusing on t…

math.AC2026

Regularity of Squarefree Powers of Edge Ideals of Whiskered Cycles

Sanjoy Das, Arka Ghosh, S Selvaraja

Let $G$ be a finite simple graph and let $I (G)$ denote its edge ideal. For $q \geq 1$ , the $q$ -th squarefree power $I (G)^{[q]}$ is generated by squarefree monomials corresponding to…

math.AC2025

Linear resolution of connected graph ideals and their powers

Arka Ghosh, S Selvaraja

For a finite simple graph $G$ and an integer $r \geq 1$ , the $r$ -connected ideal $I_{r} (G)$ is the squarefree monomial ideal generated by the vertex sets of connected induced subgraph…

cs.LO2025

Computability of Equivariant Gröbner bases

Arka Ghosh, Aliaume Lopez

Let $K$ be a field, $X$ be an infinite set (of indeterminates), and $G$ be a group acting on $X$ . An ideal in the polynomial ring $\mathbb{K}…

math.CO2025

Shellability of Higher Independence Complexes of Graphs

Arka Ghosh, S Selvaraja

This paper investigates the shellability of $r$ -independence complexes $I_{r} (G)$ , a generalization of classical independence complexes introduced by Paolini and Salvetti.…

math.NT2024

Solution of certain Diophantine equations in Gaussian integers

Arkabarata Ghosh

In this article, we show that the quartic Diophantine equations $x^{4} \pm pq y^{4} = \pm z^{2}$ and $x^{4} \pm pq y^{4} = \pm i z^{2}$ have only trivial solutions for some primes $p$ and $q$ sati…