40 citations · 95 across the 43 of their papers we have counts for
55 papers
Minimal examples of Cohen-Macaulay independence complexes that fail to be shellable or vertex decomposable
Adam Van Tuyl
We report on an exhaustive census of all 1,006,700,565 connected graphs on vertices to find the minimal examples of graphs whose independence complexes are Cohen-Macaulay but…
Edge codes constructed from unicyclic graphs
Sara Asensio, Giulia Gaggero, Naveena Ragunathan +2
Jaramillo-Velez recently introduced edge codes, a new class of toric evaluation codes constructed from the edges of a (hyper)graph . In the case that is…
Geometrically vertex decomposable star configurations
Susan M. Cooper, Emanuela Marangone, Elena Guardo +1
The goal of this paper is to determine how the family of ideals of star configurations intersects with the class of geometrically vertex decomposable ideals. The main result of thi…
Trivariate Splines on Fans of Hyperplane Arrangements and Koszul Homology
Carles Checa, Michael DiPasquale, Pablo Mazón +5
We study the space of splines where denotes a smoothness distribution and is the fan of a central hyperplan…
The van der Waerden Simplicial Complex and its Lefschetz Properties
Naveena Ragunathan, Adam Van Tuyl
The van der Waerden simplicial complex, denoted , is the simpicial complex whose facets correspond to the arithmetic progressions of length in the set $\{1,\ldo…
Comparing the -number and -polynomials of edge ideals
Kamalesh Saha, Adam Van Tuyl
In this paper, we compare the -numbers and the degree of the -polynomials associated with edge ideals of connected graphs. We prove that the -number can…
Sign patterns which require or allow the strong multiplicity property
Abhilash Saha, Leona Tilis, Kevin N. Vander Meulen +1
We initiate a study of sign patterns that require or allow the non-symmetric strong multiplicity property (nSMP). We show that all cycle patterns require the nSMP, regardless of th…
The Global Diffusion Limit for the Space Dependent Variable-Order Time-Fractional Diffusion Equation
Christopher N. Angstmann, Daniel S. Han, Bruce I. Henry +2
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous time random walks with exponential and heavy-tailed waiting time di…
Spheres and balls as independence complexes
Susan M. Cooper, Sara Faridi, Thiago Holleben +2
The terms "whiskering", and more generally "grafting", refer to adding generators to any monomial ideal to make the resulting ideal Cohen-Macaulay. We investigate the independence…
Partial Betti splittings with applications to binomial edge ideals
A. V. Jayanthan, Aniketh Sivakumar, Adam Van Tuyl
We introduce the notion of a partial Betti splitting of a homogeneous ideal, generalizing the notion of a Betti splitting first given by Francisco, Hà, and Van Tuyl. Given a homoge…
Three invariants of geometrically vertex decomposable ideals
Thai Thanh Nguyen, Jenna Rajchgot, Adam Van Tuyl
We study three invariants of geometrically vertex decomposable ideals: the Castelnuovo-Mumford regularity, the multiplicity, and the -invariant. We show that these invariants ca…
Conditions for Virtually Cohen--Macaulay Simplicial Complexes
Jay Yang, Adam Van Tuyl
A simplicial complex is a virtually Cohen-Macaulay simplicial complex if its associated Stanley-Reisner ring has a virtual resolution, as defined by Berkesch, Erman, and Sm…
Fröberg's Theorem, vertex splittability and higher independence complexes
Priyavrat Deshpande, Amit Roy, Anurag Singh +1
A celebrated theorem of Fröberg gives a complete combinatorial classification of quadratic square-free monomial ideals with a linear resolution. A generalization of this theorem to…
The weak Lefschetz property of whiskered graphs
Susan M. Cooper, Sara Faridi, Thiago Holleben +2
We consider Artinian level algebras arising from the whiskering of a graph. Employing a result by Dao-Nair we show that multiplication by a general linear form has maximal rank in…
Down-left graphs and a connection to toric ideals of graphs
Jennifer Biermann, Beth Anne Castellano, Marcella Manivel +2
We introduce a family of graphs, which we call down-left graphs, and study their combinatorial and algebraic properties. We show that members of this family are well-covered, …
Comparing invariants of toric ideals of bipartite graphs
Kieran Bhaskara, Adam Van Tuyl
Let be a finite simple graph and let denote its associated toric ideal in the polynomial ring . For each integer , we completely determine all the possible va…
Condition Numbers of Hessenberg Companion Matrices
Michael Cox, Kevin N. Vander Meulen, Adam Van Tuyl +1
The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion ma…
The GeometricDecomposability package for Macaulay2
Mike Cummings, Adam Van Tuyl
Using the geometric vertex decomposition property first defined by Knutson, Miller, and Yong, a recursive definition for geometrically vertex decomposable ideals was given by Klein…
Geometric vertex decomposition and liaison for toric ideals of graphs
Mike Cummings, Sergio Da Silva, Jenna Rajchgot +1
The geometric vertex decomposability property for polynomial ideals is an ideal-theoretic generalization of the vertex decomposability property for simplicial complexes. Indeed, a…
Powers of componentwise linear ideals: The Herzog--Hibi--Ohsugi Conjecture and related problems
Huy Tai Ha, Adam Van Tuyl
In 1999 Herzog and Hibi introduced componentwise linear ideals. A homogeneous ideal is componentwise linear if for all non-negative integers , the ideal generated by the hom…
Virtual resolutions of points in
Megumi Harada, Maryam Nowroozi, Adam Van Tuyl
We explore explicit virtual resolutions, as introduced by Berkesch, Erman, and Smith, for ideals of sets of points in . Specifically, we describe…
Powers of Principal -Borel ideals
Eduardo Camps Moreno, Craig Kohne, Eliseo Sarmiento +1
Fix a poset on . A -Borel monomial ideal is a monomial ideal whose monomials are closed under the Borel-like mov…
Homological invariants of Cameron--Walker graphs
Takayuki Hibi, Hiroju Kanno, Kyouko Kimura +2
Let be a finite simple connected graph on and the polynomial ring in variables over a field . The edge ideal of is the ideal o…
Splittings of Toric Ideals
Giuseppe Favacchio, Johannes Hofscheier, Graham Keiper +1
Let be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal can be "split" into the sum of two smaller toric…