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Priya Das

Publications and source records attributed to Priya Das.

5 recordsLinked to original sources
arXiv2024

The First Syzygy of Hibi Rings Associated with Planar distributive lattices

Let $\mathcal{L}$ be a finite distributive lattice and $S=K[x_α: α\in \mathcal{L}]$ be a polynomial ring over a field $K$ and $I=\langle x_αx_β- x_{α\vee β} x_{α\wedgeβ} : α\nsim β,α,β\in {\mathcal{L}} \rangle$ an ideal of $S$. In this article we describe the first syzygy of the Hibi ring $R[\mathcal{L}]=S/I$, for a planar distributive lattice $\mathcal{L}$. We also derive an exact formula for the first Betti number of a planar distributive lattice. We give a characterization of planar distributive lattices for which the first syzygy is linear.

math.AC↗
arXiv2022

Bounds for the regularity of product of edge ideals

Let $I$ and $J$ be edge ideals in a polynomial ring $R = \mathbb{K}[x_1,\ldots,x_n]$ with $I \subseteq J$. In this paper, we obtain a general upper and lower bound for the Castelnuovo-Mumford regularity of $IJ$ in terms of certain invariants associated with $I$ and $J$. Using these results, we explicitly compute the regularity of $IJ$ for several classes of edge ideals. Let $J_1,\ldots,J_d$ be edge ideals in a polynomial ring $R$ with $J_1 \subseteq \cdots \subseteq J_d$. Finally, we compute the precise expression for the regularity of $J_1 J_2\cdots J_d$ when $d \in \{3,4\}$ and $J_d$ is the edge ideal of complete graph.

math.AC↗
arXiv2014

Beck's Conjecture for Power Graphs

Beck's conjecture on coloring of graphs associated to various algebraic objects has generated considerable interest in the community of discrete mathematics and combinatorics since its inception in the year 1988. The version of this conjecture for power-graphs of finite groups has been addressed and partially settled by previous authors. In this paper we answer it in the affirmative in complete generality, and, in effect, we establish a "nicer" statement on a larger class of graphs. We also clear up certain ambiguities present in the way the previous versions of the conjecture were posed.

math.CO↗
arXiv2014

Hilbert-Samuel Multiplicity of a Bipartite Graph

Let $G$ be a bipartite graph and $I(G)$ the toric ideal associated to the graph $G$. In this article we calculate Hilbert-Samuel multiplicity of the graph $G$ for which the toric ideal $I(G)$ is generated by a quadratic binomials and it satiesfies some conditions.

math.AC↗