Adam Van TuylDepartment of Mathematics and StatisticsMcMaster University Hamilton, ON, Canada L8S 4L8 vantuyl@math.mcmaster.ca 

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Ideals of Powers and Powers of Ideals: Intersecting
Algebra, Geometry, and Combinatorics.
(with E. Carlini,
H.T.
Ha, and
B. Harbourne).
Lecture Notes of the Unione Matematica Italiana, 27, Springer, 2020.

Arithmetically CohenMacaulay Sets of Points in
P^{1} x P^{1}
(with E. Guardo)
SpringerBriefs in Mathematics, Springer, 2015.
Papers in refereed journals

Wellcovered Token Graphs
(with F. Abdelmalek, E. Vander Meulen, K.N. Vander Meulen)
To appear Discussiones Mathematicae Graph Theory (2021). 
Powers of Principal QBorel Ideals
(with
Eduardo Camps Moreno,
Craig Kohne,
and Eliseo Sarmiento).
Canadian Mathematical Bulletin 65 (2022) 633652. 
On the Waldschmidt Constant of Squarefree Principal Borel Ideals
(with
Eduardo Camps Moreno,
Craig Kohne,
and Eliseo Sarmiento).
Proceedings of the American Mathematical Society 150 (2022) 4145–4157. 
Virtual resolutions of points in P^{1} x P^{1}
(with Megumi Harada and Maryam Nowroozi).
Journal of Pure and Applied Algebra 226 (2022) 107140. 
Powers of componentwise linear ideals: The HerzogHibiOhsugi Conjecture
and related problems
(with Tai Ha).
Research in Mathematical Sciences 9 (2022) Article 22. 
Regularity and hpolynomials of CameronWalker graphs
(with
T. Hibi,
K. Kimura
and
K. Matsuda).
Enumerative Combinatorics and Applications 2 (2022) Article #S2R17. 
Homological invariants of CameronWalker graphs
(with
T. Hibi,
H. Kanno,
K. Kimura
and
K. Matsuda).
Transactions of the American Mathematical Society 374 (2021) 65596582. 
Splittings of toric ideals (with
G. Favacchio,
J. Hofscheier, and
G. Keiper).
Journal of Algebra 574 (2021) 409433. 
Maximum nullity and zero forcing of circulant graphs
(with L. Duong,
B. Kroschel, M. Riddell,
and
K.N. Vander Meulen)
Special Matrices 8 (2020) 221234. 
Symbolic powers of codimension two CohenMacaulay ideals
(with
S. Cooper,
G. Fatabbi,
E. Guardo,
A. Lorenzini,
J. Migliore,
U. Nagel,
A. Seceleanu,
J. Szpond).
Communications in Algebra 48 (2020) 46634680. 
Regularity and hpolynomial of toric ideals of graphs (with
G. Favacchio,
G. Keiper).
Proceedings of the American Mathematical Society. 148 (2020) 46654677. 
Hilbert functions of schemes of double and reduced points
(with E. Carlini,
M.V. Catalisano,
and
E. Guardo).
Journal of Pure and Applied Algebra 224 (2020), 106187, 20pp. 
Betti numbers of toric ideals of graphs: a case study
(with
F. Galetto,
J. Hofscheier,
G. Keiper,
C. Kohne,
M.E.U. Paczka).
Journal of Algebra and its Applications 18 (2019) 1950226. 14pp. 
Hadamard star configurations
(with E. Carlini,
M.V. Catalisano
and
E. Guardo).
Rocky Mountain Journal of Mathematics 49 (2019), 419432. 
The regularity of some families of circulant graphs
(with M.E. UribePaczka).
Mathematics 7(7) 2019, 657. 13pp. 
A note on the van der Waerden complex (with B. Hooper).
Mathematica Scandinavica 124 (2019) 179187. 
Newton complementary
dual of fideals
(with S. Budd).
Canadian Mathematical Bulletin 62 (2019) 231241. 
Regularity and hpolynomials of edge ideals
(with
T. Hibi, and
K. Matsuda).
Electronic Journal of Combinatorics 26 (2019) #P1.22, 11pp. 
The symbolic defect of an ideal
(with F. Galetto,
A.V. Geramita,
Y.S. Shin).
Journal of Pure and Applied Algebra 223 (2019) 27092731 
Shedding vertices of vertex decomposable graphs
(with J. Baker,
K.N. Vander Meulen).
Discrete Mathematics 341(2018) 33553369. 
Distinguishing kconfigurations
(with F. Galetto,
Y.S. Shin).
Illinois Journal of Mathematics 61 (2017) 415441.
[Note this paper appeared in 2018 although it has 2017 date.] 
Refined inertia of matrix patterns (with J. Earl and
K.N. Vander
Meulen)
Electronic Journal of Linear Algebra 32 (2017) 317334. 
Bounds on the regularity of toric ideals of graphs (with
J. Biermann,
A. O'Keefe)
Advances in Applied Mathematics 85 (2017) 84102. 
Shellability, vertex decomposability, and the lexicographical
products
of graphs (with
K.N. Vander
Meulen)
Contributions to Discrete Mathematics 12 (2017) 6368. 
The Waldschmidt constant for squarefree monomial ideals
(with C. Bocci,
S. Cooper,
E. Guardo
B. Harbourne,
M. Janssen,
U. Nagel,
A. Seceleanu,
T. Vu).
Journal of Algebraic Combinatorics 44 (2016) 875904. 
Independence complexes of wellcovered circulant graphs
(with J. Earl and
K.N. Vander
Meulen)
Experimental Mathematics 25 (2016) 441451. 
Partial coloring, vertex decomposability and sequentially CohenMacaulay simplicial complexes
(with J. Biermann,
C. Francisco, and
T. Ha)
Journal of Commutative Algebra 7 (2015) 337352.Erratum The version of this paper that appeared in Journal of Commutative Algebra has a small error in the statement in Theorem 4.6. Subsequent results are still correct, although their statements and proofs need some small changes. A corrected version appears on the arXiv.

On the Hilbert functions of sets of points
in P^{1} x P^{1} x
P^{1} (with E. Guardo)
Mathematical Proceedings of the Cambridge Philosophical Society 159 (2015) 115123. 
Plane curves containing a star configuration (with E. Carlini and
E. Guardo)
Journal of Pure and Applied Algebra 219 (2015) 34953505. 
Generalized cover ideals and the persistence property
(with
A. Bhat and
J. Biermann)
Journal of Pure and Applied Algebra 218 (2014) 16831695. 
Star configurations on generic hypersurfaces. (with E. Carlini and
E. Guardo)
Journal of Algebra 407 (2014) 120. 
CohenMacaulay Circulant Graph
(with
K.N. Vander Meulen,
and Catriona Watt)
Communications in Algebra 42 (2014) 18961910.
Erratum: On page 1902, the fvector and hvector on line 4 should be (1,11,33,22), respectively, (1,8,14,1). In Example 6.3, it should read G[H] = C_{10}(1,2,3,5) and H[G] = C_{10}(1,4,5). Unknown to us at the time, Theorem 4.65 of Hoshino's Ph.D. thesis contained the equivalence of Theorem 3.4 (ii) and (iv). Our Theorem 3.7 also answers Conjecture 4.68 of Hoshino's thesis.

Balanced vertex decomposable simplicial
complexes and their hvectors (with
J. Biermann)
Electronic Journal of Combinatorics 20 (2013) #P15. 
Asymptotic resurgences for ideals of positive dimensional subschemes
of projective space (with
E. Guardo and
B. Harbourne)
Advances in Mathematics 246 (2013) 114127. 
Fat lines in P^{3}: powers versus symbolic powers
(with
E. Guardo and
B. Harbourne)
Journal of Algebra 390 (2013) 221230. 
Symbolic powers versus regular
powers of ideals of general points in P^{1} x P^{1}
(with
E. Guardo and
B. Harbourne)
Canadian Journal of Mathematics 65 (2013) 823842. 
Revisiting the
spreading and covering numbers
(with Ben Babcock)
Australasian Journal of Combinatorics 56 (2013) 7784. 
Bounding invariants of fat points using a coding theory construction
(with S. Tohaneanu)
Journal of Pure and Applied Algebra 217 (2013) 269279. 
Separators of Arithmetically CohenMacaulay
fatpoints in P^{1} x P^{1}
(with E. Guardo)
Journal of Commutative Algebra 4 (2012) 255268. 
Classifying ACM sets of points in P^{1} x P^{1} via
separators
(with E. Guardo)
Archiv der Mathematik 99 (2012) 3336. 
Potentially Nilpotent Patterns and the NilpotentJacobian Method.
(with H. Bergsma,
K.N. Vander Meulen)
Linear Algebra and its Applications 436 (2012) 44334445. 
Structure of nilpotent matrices over fields. (with N. Campbell,
K.N. Vander Meulen)
Electronic Journal of Linear Algebra 22 (2011) 931958. 
Star configuration points and generic plane curves
(with E. Carlini)
Proceedings of the American Mathematical Society 139 (2011), 41814192. 
Colorings of hypergraphs, perfect graphs, and associated primes of
powers of monomial ideals
(with C.
Francisco and H.T.Ha)
Journal of Algebra 331 (2011) 224242 
Separators of fatpoints in P^{n} x P^{m}
(with E. Guardo)
Journal of Pure and Applied Algebra 215 (2011) 19901998. 
Separators of fatpoints in P^{n}
(with E. Guardo,
L. Marino)
Journal of Algebra 324 (2010) 14921512. 
Associated primes of monomial ideals and odd holes
in graphs
(with C.
Francisco and H.T.
Ha)
Journal of Algebraic Combinatorics 32 (2010) 287301. 
A conjecture on critical graphs and
connections to the persistence of associated primes.
(with C.
Francisco and H.T.
Ha)
Discrete Mathematics 310 (2010) 21762182. 
Algebraic properties of the path ideal of a tree
(with J. He)
Communications in Algebra 38 (2010) 17251742. 
Simplicial complexes and Macaulay's inverse systems
(with
F. Zanello)
Mathematische Zeitschrift 265 (2010) 151160. 
Sequentially CohenMacaulay bipartite graphs: vertex
decomposability and regularity
Archiv der Mathematik 93 (2009) 451459. 
Zerononzero patterns for nilpotent matrices over finite fields
(with K.N. Vander Meulen)
The Electronic Journal of Linear Algebra 18 (2009) 628648. 
Splittings of monomial ideals (with C.
Francisco and H.T.
Ha)
Proceedings American Mathematical Society 137 (2009) 32713282. 
Shellable graphs and sequentially CohenMacaulay bipartite graphs
(with R.
Villarreal)
Journal of Combinatorial Theory, Series A 115 (2008) 799814. 
ACM sets of points in multiprojective space (with E. Guardo)
Collectanea Mathematica 59 (2008) 191213. 
Separators of points in
a multiprojective space (with E. Guardo)
Manuscripta Mathematica 126 (2008) 99113. 
Monomial ideals, edge ideals of hypergraphs, and their graded Betti
numbers (with H.T. Ha)
Journal of Algebraic Combinatorics 27 (2008) 215245. 
Resolutions of squarefree monomial ideals via facet ideals: a survey
(with H.T. Ha)
Contemporary Mathematics. 448 (2007) 91117. 
Some families of componentwise linear monomial
ideals (with
C. Francisco)
Nagoya Mathematical Journal 187 (2007) 115156. 
The minimal resolutions of double points in P^{1} x
P^{1}
with ACM support
(with E. Guardo)
J. Pure Appl. Algebra 211 (2007) 784800.
See the CoCoA and Macaulay 2 code for the algorithm in this paper. 
Sequentially CohenMacaulay Edge Ideals
(with C.
Francisco)
Proceedings American Mathematical Society 135 (2007) 23272337. 
On the linear strand of an
edge ideal (with M.
Roth)
Communications in Algebra 35 (2007) 821832. 
Splittable ideals and the resolutions of monomial
ideals (with H.T.
Ha)
Journal of Algebra 309 (2007) 405425. 
Multigraded regularity: coarsenings and resolutions
(with J. Sidman,
H. Wang).
Journal of Algebra 301 (2006) 703727. 
Multigraded regularity: syzygies and fat points (with
J. Sidman).
Beitrage zur Algebra und Geometrie 47 (2006) 6787.
Note: Due to a mixup, the wrong version ended up in the journal;
the final version can only be found in the journal website. 
Some results on fat points
whose
support is a complete intersection minus a point (with E. Guardo).
In Projective Varieties with Unexpected Properties. de Gruyter (2005) 257266. 
An appendix to a paper of Catalisano, Geramita,
Gimigliano: the Hilbert function of generic sets of 2fat points in
P^{1} x
P^{1} .
In Projective Varieties with Unexpected Properties. de Gruyter (2005) 109112. 
Powers of complete intersections: graded
Betti numbers and applications (with E. Guardo).
Illinois J. Math. 49 (2005) 265279. 
On the defining ideal of a set of points in
multiprojective space.
Journal of the London Math. Soc. 72 (2005) 7390. 
Fat points of P^{1}
x P^{1} and their Hilbert Functions (with E. Guardo).
Canad. J. Math 56 (2004) 716741 
The regularity of points in multiprojective
spaces (with H.T.
Ha).
J. Pure Appl. Algebra 187 (2004) 153167. 
The Hilbert function of ACM
set of points in P^{n}1 x ... x
P^{n}k.
Journal of Algebra 264 (2003) 420441. 
The border of the Hilbert function of a set of points in
P^{n}1 x ... x P^{n}k.
J. Pure Appl. Algebra 176 (2002) 223247. 
Computing the Spreading and Covering Numbers (with E. Carlini,
H.T. Ha).
Communications in Algebra 29 (2001) 56875699. 
Fat Points on a grid in P^{2} (with M. Buckles,
E. Guardo).
Matematiche (Catania) 55 (2000), no. 1, 169189 (2001). 
Fat Points on a generic
almost complete intersection (with M. Buckles, E. Guardo).
Matematiche (Catania) 55 (2000), no. 1, 191202 (2001).
Some of these preprints are avaiblable at Mathematics ArXiv.

Geometric vertex decomposition and liaison for toric ideals of graphs.
(with
M. Cummings,
S. Da Silva,
J. Rajchgot)
Preprint (2022).
 (with C.
Francisco and
A. Hoefel)
EdgeIdeals: a package for (hyper)graphs.
The Journal of Software for Algebra and Geometry 1 (2009) 14.
Here is the Macaulay 2 code for this package.

Chromatic numbers via commutative algebra.
CMS Notes 15 (2019) 1415. 
A Beginner's Guide to Edge and Cover Ideals
In Monomial Ideals, Computations and Applications
Lecture Notes in Mathematics Volume 2083, 2013, pp 6394
Papers in nonrefereed journals
 Tutorial 2: A Chess Puzzle (with E. Carlini, H.T. Ha).
In COCOA VI, Proceedings of the International School, Queen's Papers in Pure and Appl. Math. 120 (2001) 215221.  Tutorial 3: Hilbert Function of Points (with
E. Carlini, H.T. Ha).
In COCOA VI, Proceedings of the International School, Queen's Papers in Pure and Appl. Math. 120 (2001) 227237.  Tutorial 5:
The Ideal Generation Conjecture (with
E. Carlini, H.T. Ha)
In COCOA VI, Proceedings of the International School, Queen's Papers in Pure and Appl. Math. 120 (2001) 245262.  Tutorial 6: The Minimal Resolution Conjecture (with
E. Carlini, H.T. Ha).
In COCOA VI, Proceedings of the International School, Queen's Papers in Pure and Appl. Math. 120 (2001) 263273. 
The graph and the image of a rational map
from P^{n} to P^{m} (with H.T. Ha).
In The Curves Seminar at Queen's, Vol XII, Queen's Papers in Pure and Appl. Math. 114 (1998) 141162.
Unpublished Papers
 The Field of
NTorsion
Points of an Elliptic Curve (2001).
An unpublished paper containing some results of my Master's thesis; this is the final version.
Theses
 Sets of Points in
MultiProjective Spaces
and their Hilbert Function.
(2001) Ph.D. thesis, Queen's University. (PDF file) 
The Field of NTorsion points of an Elliptic Curve over a Finite
Field.
(1997) M.Sc. thesis, Queen's University. (PDF file) 
An Introduction to the Theory and Applications of Continued Fractions.
(1997) B.Sc. thesis, Calvin College. (PDF file)
Reviews
A list of my reviews for Mathematical Reviews. (Need access to MathSciNet)