Searcharxiv⌕ Search

arXiv subjects

Marie Amalore Nambi

Publications and source records attributed to Marie Amalore Nambi.

7 recordsLinked to original sources
arXiv2026

On Conjecture of Binomial Edge Ideals of Linear Type

An ideal $I$ of a commutative ring $R$ is said to be of linear type when its Rees algebra and symmetric algebra exhibit isomorphism. In this paper, we investigate the conjecture put forth by Jayanthan, Kumar, and Sarkar (2021) that if $G$ is a tree or a unicyclic graph, then the binomial edge ideal of $G$ is of linear type. Our investigation validates this conjecture for trees. However, our study reveals that not all unicyclic graphs adhere to this conjecture.

math.AC↗
arXiv2026

Squarefree powers of closed neighborhood ideals

In this article, we characterize all trees whose highest non-vanishing squarefree power of the closed neighborhood ideal is componentwise linear. In addition, we investigate the Castelnuovo-Mumford regularity of the $ν$-th squarefree power of the closed neighborhood ideal of trees and show that this number can be arbitrarily larger than the degree of the ideal. Finally, we give a formula for the regularity of $ν$-th squarefree power of the closed neighborhood ideal of caterpillar graphs.

math.AC↗
arXiv2026

(Almost) Complete Intersection Lovász-Saks-Schrijver ideals and regularity of their powers

We discuss the property of (almost) complete intersection of LSS-ideals of graphs of some special forms, like trees, unicyclic, and bicyclic graphs. Further, we give a sufficient condition for the complete intersection property of twisted LSS-ideals in terms of a new graph theoretical invariant called twisted positive matching decomposition number denoted by tpmd.

math.AC↗
arXiv2025

On Positive Matching Decomposition Conjectures of Hypergraphs

In this paper, we prove the conjectures of Gharakhloo and Welker (2023) that the positive matching decomposition number (pmd) of a $3$-uniform hypergraph is bounded from above by a polynomial of degree $2$ in terms of the number of vertices. Moreover, we derive a lower bound for pmd specifically for complete $3$-uniform hypergraphs. Additionally, we obtain an upper bound for pmd of $r$-uniform hypergraphs. For a $r$-uniform hypergraphs $H=(V,E)$ such that $\lvert e_i\cap e_j\rvert \leq 1$ for all $e_i,e_j \in E$, we give a characterization of positive matching in terms of strong alternate closed walks. For a specific class of hypergraphs, we classify the radical and complete intersection Lovász$-$Saks$-$Schrijver ideals.

math.AC↗
arXiv2025

Ideals generated by corner-interval minors

In this article, we study binomial ideals generated by an arbitrary collection of corner-interval $2$-minors of a generic matrix. We determine the minimal prime ideals of such ideals and characterize their radicality in the special case of corner minors. Moreover, we discuss connectivity properties of contingency tables in algebraic statistics. We compute the Hilbert-Poincaré polynomial of the ideal generated by the set of all corner-interval minors and we derive the formula for the regularity in the case of corner minors.

math.AC↗
arXiv2024

Regularity of powers of d-sequence (parity) binomial edge ideals of unicycle graphs

We classify all unicycle graphs whose edge-binomials form a $d$-sequence, particularly linear type binomial edge ideals. We also classify unicycle graphs whose parity edge-binomials form a $d$-sequence. We study the regularity of powers of (parity) binomial edge ideals of unicycle graphs generated by $d$-sequence (parity) edge-binomials.

math.AC↗