Selvi Kara

activity

20172026

most citedRegularity of Powers of Unicyclic Graphs

9 citations · 16 across the 17 of their papers we have counts for

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17 papers · 1 filter

math.AC2026

Edge ideals of gapfree graphs with matching number $3$

Nursel Erey, Tài Huy Hà, Takayuki Hibi +2

We prove that if $G$ is a gapfree graph with matching number $3$ , then every power $I (G)^{q}$ , $q \geq 2$ , of its edge ideal has linear quotients, and hence a linear resolution. Our ap…

math.AC2026

Graded Betti numbers of graded Möbius algebras of uniform matroids

Louiza Fouli, Sean Grate, Selvi Kara +5

Graded Möbius algebras were a key tool in the proof of the Dowling-Wilson Top Heavy Conjecture. They are commutative algebras whose Hilbert functions recover the Whitney numbers of…

math.AC2026

Algebraic Invariants of Edge Ideals Under Suspension

Selvi Kara, Dalena Vien

The central question of this paper is: how do algebraic invariants of edge ideals change under natural graph operations? We study this question through the lens of suspensions. The…

math.AC2026

Neural codes via homological invariants of polarized neural ideals

Selvi Kara, Ellie Lew

For a neural code $C \subseteq F_{2}^{n}$ , polarizing the canonical form generators of the neural ideal $J_{C}$ yields a squarefree monomial ideal $\mathcal{…

math.AC2026

Realizable (reg, deg h)-Pairs for Cover Ideals via Independence Polynomials

Jennifer Biermann, Trung Chau, Selvi Kara +4

Let $G$ be a finite simple graph on $n$ vertices and set $R = k [x_{1}, \dots, x_{n}]$ , with edge ideal $I (G)$ and cover ideal $J (G)$ . We give an explicit description of the $h$ -polynom…

math.AC2025

Computation of dominant ideals

Anna Maria Bigatti, Nursel Erey, Selvi Kara +4

We consider the problem of determining whether a monomial ideal is dominant. This property is critical for determining for which monomial ideals the Taylor resolution is minimal. W…

math.AC2024

Gapfree graphs and powers of edge ideals with linear quotients

Nursel Erey, Sara Faridi, Tài Huy Hà +3

Let $I (G)$ be the edge ideal of a gapfree graph $G$ . An open conjecture of Nevo and Peeva states that $I (G)^{q}$ has linear resolution for $q ≫ 0$ . We present a promising approach t…

math.AC2024

Degree of $h$ -polynomials of edge ideals

Jennifer Biermann, Selvi Kara, Augustine O'Keefe +2

In this paper, we investigate the degree of $h$ -polynomials of edge ideals of finite simple graphs. In particular, we provide combinatorial formulas for the degree of the $h$ -polyn…

math.AC2024

Minimal Cellular Resolutions of Path Ideals

Trung Chau, Selvi Kara, Kyle Wang

In this paper, we prove that the path ideals of both paths and cycles have minimal cellular resolutions. Specifically, these minimal free resolutions coincide with the Barile-Macch…

math.AC2023

The MorseResolutions package for Macaulay2

Trung Chau, Selvi Kara, Augustine O'Keefe

Using discrete Morse theory, Batzies and Welker introduced Morse resolutions of monomial ideals. In this note, we present the {\it Macaulay2} package {\tt MorseResolutions} for wor…

math.AC2022★ 7 cited

Barile-Macchia resolutions

Trung Chau, Selvi Kara

We construct cellular resolutions for monomial ideals via discrete Morse theory. In particular, we develop an algorithm to create homogeneous acyclic matchings and we call the cell…

math.AC2021

Toric Ideals of Weighted Oriented Graphs

Jennifer Biermann, Selvi Kara, Kuei-Nuan Lin +1

Given a vertex-weighted oriented graph, we can associate to it a set of monomials. We consider the toric ideal whose defining map is given by these monomials. We find a generating…

math.AC2020

Multi-Rees Algebras of Strongly Stable Ideals

Selvi Kara, Kuei-Nuan Lin, Gabriel Sosa

We prove that the multi-Rees algebra $R (I_{1} \oplus \dots \oplus I_{r})$ of a collection of strongly stable ideals $I_{1}, \dots, I_{r}$ is of fiber type. In particular, we pr…

math.AC2020

Betti numbers of weighted oriented graphs

Beata Casiday, Selvi Kara

Let $D$ be a weighted oriented graph and $I (D)$ be its edge ideal. In this paper, we investigate the Betti numbers of $I (D)$ via upper-Koszul simplici…

math.AC2020

On algebraic and combinatorial properties of weighted simplicial complexes

Selvi Kara

Weighted simplicial complexes (WSCs) are powerful tools for describing weighted cloud data or networks with weighted nodes. In this paper, we propose a novel approach to study WSCs…

math.AC2019

Algebraic invariants of weighted oriented graphs

Selvi Kara, Jennifer Biermann, Kuei-Nuan Lin +1

Let $D$ be a weighted oriented graph and let $I (D)$ be its edge ideal in a polynomial ring $R$ . We give the formula of Castelnuovo-Mumford regularity of $R/I(\m…

math.AC2017★ 9 cited

Regularity of Powers of Unicyclic Graphs

Ali Alilooee, Selvi Kara, S. Selvaraja

Let $G$ be a finite simple graph and $I (G)$ denote the corresponding edge ideal. In this paper we prove that if $G$ is a unicyclic graph then for all $s \geq 1$ the regularity of $…

Edge ideals of gapfree graphs with matching number 3

Graded Betti numbers of graded Möbius algebras of uniform matroids

Algebraic Invariants of Edge Ideals Under Suspension

Neural codes via homological invariants of polarized neural ideals

Realizable (reg, deg h)-Pairs for Cover Ideals via Independence Polynomials

Computation of dominant ideals

Gapfree graphs and powers of edge ideals with linear quotients

Degree of h-polynomials of edge ideals

Minimal Cellular Resolutions of Path Ideals

The MorseResolutions package for Macaulay2

Barile-Macchia resolutions

Toric Ideals of Weighted Oriented Graphs

Multi-Rees Algebras of Strongly Stable Ideals

Betti numbers of weighted oriented graphs

On algebraic and combinatorial properties of weighted simplicial complexes

Algebraic invariants of weighted oriented graphs

Regularity of Powers of Unicyclic Graphs

Edge ideals of gapfree graphs with matching number $3$

Degree of $h$ -polynomials of edge ideals