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Chitra Venugopal

Publications and source records attributed to Chitra Venugopal.

6 recordsLinked to original sources
arXiv2026

Multiplicity of negative one of independence polynomials of graphs

We initiate the study of the multiplicity of negative one of independence polynomials of graphs. In this article, we simply refer to this as the \emph{multiplicity} of a graph. As applications, we provide a graph-theoretic description of trees whose independence complexes are contractible, give a new sufficient condition for independence polynomials of graphs to be log-concave, and finally, determine possible pairs $(\operatorname{mult}_{-1}P_G, \alpha(G))$, where $P_G$ denotes the independence polynomial of $G$, and $\alpha(G)$ the independence number. The study of the pairs $(\operatorname{mult}_{-1}P_G, \alpha(G))$ is equivalent to finding all pairs of the numerator degree and denominator degree of the Hilbert series of the edge ideal of $G$. We also use spectral graph theory to obtain results on the multiplicity of line graphs of forests. Finally, we give some translations and applications in combinatorial commutative algebra.

math.CO↗
arXiv2026

Free Resolutions of Symmetric Algebras of Ideals with Deviation Two

For a graded ideal I in a graded ring, the deviation of I is defined as the difference between the minimal number of generators of I and its grade. In this article, we provide bigraded free resolutions of the symmetric algebras for specific classes of ideals of deviation two. Additionally, we study the regularity of powers of deviation two ideals generated by d-sequences. In particular, we examine the powers of Huneke-Ulrich ideals and find bounds on their regularity.

math.AC↗
arXiv2024

Almost Complete Intersections: Regularity of powers and Rees algebra

An almost complete intersection ideal can be seen as a $d$-sequence ideal with the minimal number of generators being one more than its height. In this paper, we give exact formulas for the regularity of powers of graded almost complete intersection ideals satisfying certain conditions. We also present the minimal bigraded free resolutions of Rees algebras associated with linear type ideals having one generator more than their grade and study the properties of Cohen-Macaulayness, Koszulness associated to their diagonals.

math.AC↗
arXiv2023

Some classes of sequences of Linear Type

Given a graded ring $A$ and a homogeneous ideal $I$, the ideal is said to be of linear type if the Rees algebra of $I$ is isomorphic to the symmetric algebra of $I$. In general, $y$-regularity of Rees algebra of $I$ is $0 \Rightarrow$ $I$ is generated by a $d$-sequence $\Rightarrow I$ is of linear type. We show that $d$-sequence ideals represent a significantly smaller subset of ideals of linear type in terms of $y$-regularity. Moreover, we identify a class of $d$-sequences whose arbitrary powers generate ideals of Gr\"obner linear type. Notably, while $d$-sequences are inherently weak $d$-sequences, we highlight a specific class of algebras where weak $d$-sequences are indeed $d$-sequences.

math.AC↗
arXiv2023

Rees algebra of maximal order Pfaffians and its diagonal subalgebras

Given a skew-symmetric matrix $X$, the Pfaffian of $X$ is defined as the square root of the determinant of $X$. In this article, we give the explicit defining equations of the Rees algebra of a Pfaffian ideal $I$ generated by the maximal order Pfaffians of a generic skew-symmetric matrix. We further prove that all diagonal subalgebras of the corresponding Rees algebra of $I$ are Koszul. We also look at Rees algebras of Pfaffian ideals of linear type associated with certain sparse skew-symmetric matrices. In particular, we consider the tridiagonal matrices and identify the corresponding Pfaffian ideals to be of Gr\"obner linear type and as the vertex cover ideals of unmixed bipartite graphs. As an application of our results, we conclude that all their ordinary and symbolic powers have linear quotients.

math.AC↗