selected scholarly activity
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books
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chapters
- Resolutions of square-free monomial ideals via facet ideals: a survey. Contemporary Mathematics. 91-117. 2007
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conferences
- A Beginner’s Guide to Edge and Cover Ideals. Lecture Notes in Mathematics. 63-94. 2013
- Edge Ideals Using Macaulay2. Lecture Notes in Mathematics. 95-105. 2013
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journal articles
- Hadamard products and binomial ideals. Journal of Pure and Applied Algebra. 228:107568-107568. 2024
- Condition numbers of Hessenberg companion matrices. Czechoslovak Mathematical Journal. 74:191-209. 2024
- The GeometricDecomposability package for Macaulay2. The Journal of Software forAlgebra and Geometry: Macaulay2. 14:41-50. 2024
- Correction to: Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers [J. ALGEBRAIC COMBIN. 27 (2008), NO. 2, 215-245]. Journal of Algebraic Combinatorics. 58:325-328. 2023
- Well-Covered Token Graphs. Discussiones Mathematicae - Graph Theory. 43:767-792. 2023
- Condition Numbers of Hessenberg Companion Matrices. Czechoslovak Mathematical Journal. 2023
- Comparing invariants of toric ideals of bipartite graphs. Proceedings of the American Mathematical Society, Series B. 10:219-232. 2023
- Geometric vertex decomposition and liaison for toric ideals of graphs. Algebraic Combinatorics. 6:965-997. 2023
- Virtual resolutions of points in P 1 × P 1. Journal of Pure and Applied Algebra. 226:107140-107140. 2022
- On the Waldschmidt constant of square-free principal Borel ideals. Proceedings of the American Mathematical Society. 150:4145-4157. 2022
- Powers of Principal Q-Borel ideals. Canadian Mathematical Bulletin. 65:633-652. 2022
- Powers of componentwise linear ideals: the Herzog–Hibi–Ohsugi conjecture and related problems. Research in Mathematical Sciences. 9. 2022
- Homological invariants of Cameron–Walker Graphs. Transactions of the American Mathematical Society. 374:6559-6582. 2021
- Splittings of toric ideals. Journal of Algebra. 574:409-433. 2021
- Maximum nullity and zero forcing of circulant graphs. Special Matrices. 8:221-234. 2020
- Regularity and h-polynomials of toric ideals of graphs. Proceedings of the American Mathematical Society. 148:4665-4677. 2020
- Symbolic powers of codimension two Cohen-Macaulay ideals. Communications in Algebra. 48:4663-4680. 2020
- Hilbert functions of schemes of double and reduced points. Journal of Pure and Applied Algebra. 224:106187-106187. 2020
- Betti numbers of toric ideals of graphs: A case study. Journal of Algebra and its Applications. 18:1950226-1950226. 2019
- The Regularity of Some Families of Circulant Graphs. Mathematics. 7:657-657. 2019
- Newton Complementary Duals of -Ideals. Canadian Mathematical Bulletin. 62:231-241. 2019
- The symbolic defect of an ideal. Journal of Pure and Applied Algebra. 223:2709-2731. 2019
- Hadamard star configurations. Rocky Mountain Journal of Mathematics. 49:419-432. 2019
- A note on the van der Waerden complex. Mathematica Scandinavica. 124:179-187. 2019
- Regularity and h-polynomials of edge ideals. Electronic Journal of Combinatorics. 26:1-11. 2019
- Shedding vertices of vertex decomposable well-covered graphs. Discrete Mathematics. 341:3355-3369. 2018
- Distinguishing k-configurations. Illinois Journal of Mathematics. 61:415-441. 2017
- Refined Inertia of Matrix Patterns. Electronic Journal of Linear Algebra. 32:317-344. 2017
- Bounds on the regularity of toric ideals of graphs. Advances in Applied Mathematics. 85:84-102. 2017
- SHELLABILITY, VERTEX DECOMPOSABILITY, AND LEXICOGRAPHICAL PRODUCTS OF GRAPHS. Contributions to Discrete Mathematics. 12:63-68. 2017
- The Waldschmidt constant for squarefree monomial ideals. Journal of Algebraic Combinatorics. 44:875-904. 2016
- Independence Complexes of Well-Covered Circulant Graphs. Experimental Mathematics. 25:441-451. 2016
- Shedding vertices of vertex decomposable graphs 2016
- Partial coloring, vertex decomposability and sequentially Cohen-Macaulay simplicial complexes. Journal of Commutative Algebra. 7:337-352. 2015
- Plane curves containing a star configuration. Journal of Pure and Applied Algebra. 219:3495-3505. 2015
- On the Hilbert functions of sets of points in P^1 x P^1 x P^1. Mathematical Proceedings of the Cambridge Philosophical Society. 159:115-123. 2015
- Partial coloring, vertex decomposability, and sequentially cohen-macaulay simplicial complexes. Journal of Commutative Algebra. 7:337-352. 2015
- Generalized cover ideals and the persistence property. Journal of Pure and Applied Algebra. 218:1683-1695. 2014
- Star configurations on generic hypersurfaces. Journal of Algebra. 407:1-20. 2014
- Cohen–Macaulay Circulant Graphs. Communications in Algebra. 42:1896-1910. 2014
- Asymptotic resurgences for ideals of positive dimensional subschemes of projective space. Advances in Mathematics. 246:114-127. 2013
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Fat lines in
- Balanced Vertex Decomposable Simplicial Complexes and their h-vectors. Electronic Journal of Combinatorics. 20. 2013
- Symbolic Powers Versus Regular Powers of Ideals of General Points in ℙ1× ℙ1. Canadian Journal of Mathematics. 65:823-842. 2013
- Revisiting the spreading and covering numbers. The Australasian Journal of Combinatorics. 56:77-84. 2013
- Bounding invariants of fat points using a coding theory construction. Journal of Pure and Applied Algebra. 217:269-279. 2013
- A beginner's guide to edge and cover ideals. Lecture Notes in Mathematics. 2083:63-94. 2013
- Edge ideals using Macaulay2. Lecture Notes in Mathematics. 2083:95-105. 2013
- Classifying ACM sets of points in via separators. Archiv der Mathematik. 99:33-36. 2012
- Potentially nilpotent patterns and the Nilpotent-Jacobian method. Linear Algebra and Its Applications. 436:4433-4445. 2012
- Separators of arithmetically Cohen-Macaulay fat points ${\bf P}^1\times {\bf P}^1$. Journal of Commutative Algebra. 4:255-268. 2012
- Star configuration points and generic plane curves. Proceedings of the American Mathematical Society. 139:4181-4192. 2011
- Structure of nilpotent matrices over fields. Electronic Journal of Linear Algebra. 22:931-958. 2011
- Separators of fat points in Pn×Pm. Journal of Pure and Applied Algebra. 215:1990-1998. 2011
- Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals. Journal of Algebra. 331:224-242. 2011
- Separators of fat points in P{double-struck}n. Journal of Algebra. 324:1492-1512. 2010
- Associated primes of monomial ideals and odd holes in graphs. Journal of Algebraic Combinatorics. 32:287-301. 2010
- A conjecture on critical graphs and connections to the persistence of associated primes. Discrete Mathematics. 310:2176-2182. 2010
- Simplicial complexes and Macaulay’s inverse systems. Mathematische Zeitschrift. 265:151-160. 2010
- Algebraic Properties of the Path Ideal of a Tree. Communications in Algebra. 38:1725-1742. 2010
- Sequentially Cohen–Macaulay bipartite graphs: vertex decomposability and regularity. Archiv der Mathematik. 93:451-459. 2009
- Splittings of monomial ideals. Proceedings of the American Mathematical Society. 137:3271-3271. 2009
- Zero-nonzero patterns for nilpotent matrices over finite fields. Electronic Journal of Linear Algebra. 18:628-648. 2009
- Shellable graphs and sequentially Cohen–Macaulay bipartite graphs. Journal of combinatorial theory. Series A. 115:799-814. 2008
- ACM sets of points in multiprojective space. Collectanea Mathematica. 59:191-213. 2008
- Separators of points in a multiprojective space. Manuscripta Mathematica. 126:99-113. 2008
- Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers. Journal of Algebraic Combinatorics. 27:215-245. 2008
- The minimal resolutions of double points in P1 × P1 with ACM support. Journal of Pure and Applied Algebra. 211:784-800. 2007
- Some Families of Componentwise Linear Monomial Ideals. Nagoya Mathematical Journal. 187:115-156. 2007
- Sequentially Cohen-Macaulay edge ideals. Proceedings of the American Mathematical Society. 135:2327-2338. 2007
- Splittable ideals and the resolutions of monomial ideals. Journal of Algebra. 309:405-425. 2007
- On the Linear Strand of an Edge Ideal. Communications in Algebra. 35:821-832. 2007
- Resolutions of square-free monomial ideals via facet ideals: A survey. Contemporary Mathematics. 448:91-+. 2007
- Multigraded regularity: Syzygies and fat points. Beitrage zur Algebra und Geometrie. 47:1-22. 2006
- Multigraded regularity: Coarsenings and resolutions. Journal of Algebra. 301:703-727. 2006
- THE DEFINING IDEAL OF A SET OF POINTS IN MULTI-PROJECTIVE SPACE. Journal of the London Mathematical Society. 72:73-90. 2005
- Powers of complete intersections: graded Betti numbers and applications. Illinois Journal of Mathematics. 49:265-279. 2005
- Fat Points in ℙ1× ℙ1and Their Hilbert Functions. Canadian Journal of Mathematics. 56:716-741. 2004
- The regularity of points in multi-projective spaces. Journal of Pure and Applied Algebra. 187:153-167. 2004
- The Hilbert functions of ACM sets of points in Pn1×⋯×Pnk. Journal of Algebra. 264:420-441. 2003
- The border of the Hilbert function of a set of points in Pn1×⋯×Pnk. Journal of Pure and Applied Algebra. 176:223-247. 2002
- The Hilbert functions of ACM sets of points in P^{n_1} x ... x P^{n_k}. Journal of Algebra. 264:420-441. 2001
- The border of the Hilbert function of a set of points in P^{n_1} x ... x P^{n_k}. Journal of Pure and Applied Algebra. 176:223-247. 2001
- COMPUTING THE SPREADING AND COVERING NUMBERS. Communications in Algebra. 29:5687-5699. 2001
- Conditions for Virtually Cohen--Macaulay Simplicial Complexes. https://arxiv.org/abs/2311.17806.
- Down-left graphs and a connection to toric ideals of graphs. https://arxiv.org/abs/2304.14528.
- Fröberg's Theorem, vertex splittability and higher independence complexes. https://arxiv.org/abs/2311.02430.
- The weak Lefschetz property of whiskered graphs. Lefschetz Properties: Current and New Directions. https://arxiv.org/abs/2306.04393.
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preprints
- Three invariants of geometrically vertex decomposable ideals 2023
- Comparing invariants of toric ideals of bipartite graphs 2023
- Hadamard Products and Binomial Ideals 2022
- Geometric vertex decomposition and liaison for toric ideals of graphs 2022
- Virtual resolutions of points in $\mathbb{P}^1 \times \mathbb{P}^1$ 2021
- On the Waldschmidt constant of square-free principal Borel ideals 2021
- Powers of Principal $Q$-Borel ideals 2020
- Well-covered Token Graphs 2020
- Homological invariants of Cameron--Walker graphs 2020
- Regularity and h-polynomials of toric ideals of graphs 2020
- Splittings of Toric Ideals 2019
- The regularity of some families of circulant graphs 2019
- Maximum nullity and zero forcing of circulant graphs 2019
- Betti numbers of toric ideals of graphs: A case study 2018
- Hilbert functions of schemes of double and reduced points 2018
- Hadamard Star Configurations 2018
- Distinguishing $\Bbbk$-configurations 2017
- Refined Inertia of Matrix Patterns 2016
- The symbolic defect of an ideal 2016
- Symbolic powers of codimension two Cohen-Macaulay ideals 2016
- Bounds on the regularity of toric ideals of graphs 2016
- The Waldschmidt constant for squarefree monomial ideals 2015
- Independence complexes of well-covered circulant graphs 2015
- Shellability, vertex decomposability, and lexicographical products of graphs 2015
- On the Hilbert functions of sets of points in P^1 x P^1 x P^1 2014
- Plane curves containing a star configuration 2013
- Cohen-Macaulay Circulant Graphs 2012
- Partial coloring, vertex decomposability, and sequentially Cohen-Macaulay simplicial complexes 2012
- Fat lines in P^3: powers versus symbolic powers 2012
- Classifying ACM sets of points in $P^1XP^1$ via separators 2012
- Star configurations on generic hypersurfaces 2012
- Asymptotic resurgences for ideals of positive dimensional subschemes of projective space 2012
- Symbolic powers versus regular powers of ideals of general points in P^1 x P^1 2011
- Potentially Nilpotent Patterns and the Nilpotent-Jacobian Method 2010
- Separators of Arithmetically Cohen-Macaulay fat points in P^1 x P^1 2010
- A conjecture on critical graphs and connections to the persistence of associated primes 2009
- Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals 2009
- Separators of fat points in P^n x P^m 2009
- Separators of fat points in P^n 2009
- Zero-nonzero patterns for nilpotent matrices over finite fields 2008
- Splittings of monomial ideals 2008
- Associated primes of monomial ideals and odd holes in graphs 2008
- Simplicial complexes and Macaulay's inverse systems 2007
- ACM sets of points in multiprojective space 2007
- Separators of points in a multiprojective space 2007
- Shellable graphs and sequentially Cohen-Macaulay bipartite graphs 2007
- The minimal resolutions of double points in P^1 x P^1 with ACM support 2006
- Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers 2006
- Resolutions of square-free monomial ideals via facet ideals: a survey 2006
- Multigraded regularity: coarsenings and resolutions 2005
- Splittable ideals and the resolutions of monomial ideals 2005
- Powers of complete intersections: graded Betti numbers and applications 2004
- Multigraded regularity: syzygies and fat points 2004
- The regularity of points in multi-projective spaces 2002
- Fat Points in P^1 x P^1 and their Hilbert Functions 2002
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presentations