9 citations · 16 across the 17 of their papers we have counts for
21 papers
Edge ideals of gapfree graphs with matching number
Nursel Erey, Tài Huy Hà, Takayuki Hibi +2
We prove that if is a gapfree graph with matching number , then every power , , of its edge ideal has linear quotients, and hence a linear resolution. Our ap…
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…
Symmetric and unimodal independence polynomials of trees
Takayuki Hibi, Selvi Kara, Dalena Vien
Given , we study the existence of a tree on vertices whose independence polynomial is symmetric and unimodal as well as the existence of a symmetric and unimodal inde…
Independence polynomials of graphs
Takayuki Hibi, Selvi Kara, Dalena Vien
In this paper, we study the independence polynomial of a finite simple graph , with emphasis on the evaluation at , symmetry, and its connection with the -poly…
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…
Neural codes via homological invariants of polarized neural ideals
Selvi Kara, Ellie Lew
For a neural code , polarizing the canonical form generators of the neural ideal yields a squarefree monomial ideal $\mathcal{…
Realizable (reg, deg h)-Pairs for Cover Ideals via Independence Polynomials
Jennifer Biermann, Trung Chau, Selvi Kara +4
Let be a finite simple graph on vertices and set , with edge ideal and cover ideal . We give an explicit description of the -polynom…
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…
Gapfree graphs and powers of edge ideals with linear quotients
Nursel Erey, Sara Faridi, Tài Huy Hà +3
Let be the edge ideal of a gapfree graph . An open conjecture of Nevo and Peeva states that has linear resolution for . We present a promising approach t…
Degree of -polynomials of edge ideals
Jennifer Biermann, Selvi Kara, Augustine O'Keefe +2
In this paper, we investigate the degree of -polynomials of edge ideals of finite simple graphs. In particular, we provide combinatorial formulas for the degree of the -polyn…
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…
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…
A Three-Regime Theorem for Flow-Firing
Sarah Brauner, Galen Dorpalen-Barry, Selvi Kara +2
Graphical chip-firing is a discrete dynamical system where chips are placed on the vertices of a graph and exchanged via simple firing moves. Recent work has sought to generalize c…
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…
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…
Rigid Gorenstein toric Fano varieties arising from directed graphs
Selvi Kara, Irem Portakal, Akiyoshi Tsuchiya
A directed edge polytope is a lattice polytope arising from root system and a finite directed graph . If every directed edge of belongs to a directed c…
Multi-Rees Algebras of Strongly Stable Ideals
Selvi Kara, Kuei-Nuan Lin, Gabriel Sosa
We prove that the multi-Rees algebra of a collection of strongly stable ideals is of fiber type. In particular, we pr…
Betti numbers of weighted oriented graphs
Beata Casiday, Selvi Kara
Let be a weighted oriented graph and be its edge ideal. In this paper, we investigate the Betti numbers of via upper-Koszul simplici…
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…
Algebraic invariants of weighted oriented graphs
Selvi Kara, Jennifer Biermann, Kuei-Nuan Lin +1
Let be a weighted oriented graph and let be its edge ideal in a polynomial ring . We give the formula of Castelnuovo-Mumford regularity of $R/I(\m…
Regularity of Powers of Unicyclic Graphs
Ali Alilooee, Selvi Kara, S. Selvaraja
Let be a finite simple graph and denote the corresponding edge ideal. In this paper we prove that if is a unicyclic graph then for all the regularity of $…