Adam Van Tuyl

Department of Mathematics and Statistics
McMaster University
Hamilton, ON, Canada
L8S 4L8
vantuyl@math.mcmaster.ca

Publications

Preprints

Software

Expository

Other

Home

Note: If there is paper you would like, but cannot get here, please contact me and I'll see what I can do.

Books

  1. 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.
  2. Arithmetically Cohen-Macaulay Sets of Points in P1 x P1 (with E. Guardo)
    SpringerBriefs in Mathematics, Springer, 2015.

Papers in refereed journals

  1. Froberg's Theorem, vertex splittability and higher independence complexes (with Priyavrat Deshpande, Amit Roy, Anurag Singh)
    To appear Journal of Commutative Algebra (2024).
  2. Down-left graphs and a connection to toric ideals of graphs (with J. Biermann, B.A. Castellano, M. Manivel, E. Petrucelli)
    To appear Involve (2024).
  3. Simplicial complexes with many facets are vertex decomposable (with Anton Dochtermann, Ritika Nair, Jay Schweig, Russ Woodroofe)
    Electronic Journal of Combinatorics 31 (2024) #P4.34.
  4. The weak Lefschetz property of whiskered graphs (with S.M. Cooper, S. Faridi, T. Holleben, L. Nicklasson)
    In: U. Nagel, K. Adiprasito, R. Di Gennaro, S. Faridi, S. Murai, S. (eds) Lefschetz Properties: Current and New Directions, Springer INdAM Series, vol 59. Springer, Singapore. 97--110.
  5. Condition Numbers of Hessenberg Companion Matrices (with M. Cox, K.N. Vander Meulen, J. Voskamp)
    Czechoslovak Mathematical Journal 74 (2024) 191-209.
  6. Hadamard Products and Binomial Ideals (with B. Atar, K. Bhaskara, A. Cook, S. Da Silva, M. Harada, J. Rajchgot, Runyue Wang, Jay Yang)
    Journal of Pure and Applied Algebra 228 (2024) 107568.
  7. Geometric vertex decomposition and liaison for toric ideals of graphs. (with M. Cummings, S. Da Silva, J. Rajchgot)
    Algebraic Combinatorics 6 (2023) 965--997.
  8. Comparing invariants of toric ideals of bipartite graphs (with K. Bhaskara)
    Proceedings of the American Mathematical, Series B 10 (2023), 219-232.
  9. Well-covered Token Graphs (with F. Abdelmalek, E. Vander Meulen, K.N. Vander Meulen)
    Discussiones Mathematicae Graph Theory 43 (2023) 762--792.
  10. Powers of Principal Q-Borel Ideals (with Eduardo Camps Moreno, Craig Kohne, and Eliseo Sarmiento).
    Canadian Mathematical Bulletin 65 (2022) 633--652.
  11. On the Waldschmidt Constant of Square-free Principal Borel Ideals (with Eduardo Camps Moreno, Craig Kohne, and Eliseo Sarmiento).
    Proceedings of the American Mathematical Society 150 (2022) 4145–4157.
  12. Virtual resolutions of points in P1 x P1 (with Megumi Harada and Maryam Nowroozi).
    Journal of Pure and Applied Algebra 226 (2022) 107140.
  13. Powers of componentwise linear ideals: The Herzog--Hibi--Ohsugi Conjecture and related problems (with Tai Ha).
    Research in Mathematical Sciences 9 (2022) Article 22.
  14. Regularity and h-polynomials of Cameron-Walker graphs (with T. Hibi, K. Kimura and K. Matsuda).
    Enumerative Combinatorics and Applications 2 (2022) Article #S2R17.
  15. Homological invariants of Cameron--Walker graphs (with T. Hibi, H. Kanno, K. Kimura and K. Matsuda).
    Transactions of the American Mathematical Society 374 (2021) 6559--6582.
  16. Splittings of toric ideals (with G. Favacchio, J. Hofscheier, and G. Keiper).
    Journal of Algebra 574 (2021) 409--433.
  17. Maximum nullity and zero forcing of circulant graphs (with L. Duong, B. Kroschel, M. Riddell, and K.N. Vander Meulen)
    Special Matrices 8 (2020) 221--234.
  18. Symbolic powers of codimension two Cohen-Macaulay ideals (with S. Cooper, G. Fatabbi, E. Guardo, A. Lorenzini, J. Migliore, U. Nagel, A. Seceleanu, J. Szpond).
    Communications in Algebra 48 (2020) 4663--4680.
  19. Regularity and h-polynomial of toric ideals of graphs (with G. Favacchio, G. Keiper).
    Proceedings of the American Mathematical Society. 148 (2020) 4665--4677.
  20. 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.
  21. 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.
  22. Hadamard star configurations (with E. Carlini, M.V. Catalisano and E. Guardo).
    Rocky Mountain Journal of Mathematics 49 (2019), 419--432.
  23. The regularity of some families of circulant graphs (with M.E. Uribe-Paczka).
    Mathematics 7(7) 2019, 657. 13pp.
  24. A note on the van der Waerden complex (with B. Hooper).
    Mathematica Scandinavica 124 (2019) 179--187.
  25. Newton complementary dual of f-ideals (with S. Budd).
    Canadian Mathematical Bulletin 62 (2019) 231--241.
  26. Regularity and h-polynomials of edge ideals (with T. Hibi, and K. Matsuda).
    Electronic Journal of Combinatorics 26 (2019) #P1.22, 11pp.
  27. The symbolic defect of an ideal (with F. Galetto, A.V. Geramita, Y.-S. Shin).
    Journal of Pure and Applied Algebra 223 (2019) 2709--2731
  28. Shedding vertices of vertex decomposable graphs (with J. Baker, K.N. Vander Meulen).
    Discrete Mathematics 341(2018) 3355--3369.
  29. Distinguishing k-configurations (with F. Galetto, Y.-S. Shin).
    Illinois Journal of Mathematics 61 (2017) 415--441.
    [Note this paper appeared in 2018 although it has 2017 date.]
  30. Refined inertia of matrix patterns (with J. Earl and K.N. Vander Meulen)
    Electronic Journal of Linear Algebra 32 (2017) 317--334.
  31. Bounds on the regularity of toric ideals of graphs (with J. Biermann, A. O'Keefe)
    Advances in Applied Mathematics 85 (2017) 84--102.
  32. Shellability, vertex decomposability, and the lexicographical products of graphs (with K.N. Vander Meulen)
    Contributions to Discrete Mathematics 12 (2017) 63--68.
  33. 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) 875--904.
  34. Independence complexes of well-covered circulant graphs (with J. Earl and K.N. Vander Meulen)
    Experimental Mathematics 25 (2016) 441--451.
  35. Partial coloring, vertex decomposability and sequentially Cohen-Macaulay simplicial complexes (with J. Biermann, C. Francisco, and T. Ha)
    Journal of Commutative Algebra 7 (2015) 337--352.

    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.

  36. On the Hilbert functions of sets of points in P1 x P1 x P1 (with E. Guardo)
    Mathematical Proceedings of the Cambridge Philosophical Society 159 (2015) 115--123.
  37. Plane curves containing a star configuration (with E. Carlini and E. Guardo)
    Journal of Pure and Applied Algebra 219 (2015) 3495--3505.
  38. Generalized cover ideals and the persistence property (with A. Bhat and J. Biermann)
    Journal of Pure and Applied Algebra 218 (2014) 1683--1695.
  39. Star configurations on generic hypersurfaces. (with E. Carlini and E. Guardo)
    Journal of Algebra 407 (2014) 1--20.
  40. Cohen-Macaulay Circulant Graph (with K.N. Vander Meulen, and Catriona Watt)
    Communications in Algebra 42 (2014) 1896-1910.

    Erratum: On page 1902, the f-vector and h-vector on line 4 should be (1,11,33,22), respectively, (1,8,14,-1). In Example 6.3, it should read G[H] = C10(1,2,3,5) and H[G] = C10(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.

  41. Balanced vertex decomposable simplicial complexes and their h-vectors (with J. Biermann)
    Electronic Journal of Combinatorics 20 (2013) #P15.
  42. Asymptotic resurgences for ideals of positive dimensional subschemes of projective space (with E. Guardo and B. Harbourne)
    Advances in Mathematics 246 (2013) 114-127.
  43. Fat lines in P3: powers versus symbolic powers (with E. Guardo and B. Harbourne)
    Journal of Algebra 390 (2013) 221-230.
  44. Symbolic powers versus regular powers of ideals of general points in P1 x P1 (with E. Guardo and B. Harbourne)
    Canadian Journal of Mathematics 65 (2013) 823-842.
  45. Revisiting the spreading and covering numbers (with Ben Babcock)
    Australasian Journal of Combinatorics 56 (2013) 77--84.
  46. Bounding invariants of fat points using a coding theory construction (with S. Tohaneanu)
    Journal of Pure and Applied Algebra 217 (2013) 269--279.
  47. Separators of Arithmetically Cohen-Macaulay fatpoints in P1 x P1 (with E. Guardo)
    Journal of Commutative Algebra 4 (2012) 255--268.
  48. Classifying ACM sets of points in P1 x P1 via separators (with E. Guardo)
    Archiv der Mathematik 99 (2012) 33-36.
  49. Potentially Nilpotent Patterns and the Nilpotent-Jacobian Method. (with H. Bergsma, K.N. Vander Meulen)
    Linear Algebra and its Applications 436 (2012) 4433-4445.
  50. Structure of nilpotent matrices over fields. (with N. Campbell, K.N. Vander Meulen)
    Electronic Journal of Linear Algebra 22 (2011) 931-958.
  51. Star configuration points and generic plane curves (with E. Carlini)
    Proceedings of the American Mathematical Society 139 (2011), 4181--4192.
  52. 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) 224-242
  53. Separators of fatpoints in Pn x Pm (with E. Guardo)
    Journal of Pure and Applied Algebra 215 (2011) 1990-1998.
  54. Separators of fatpoints in Pn (with E. Guardo, L. Marino)
    Journal of Algebra 324 (2010) 1492-1512.
  55. Associated primes of monomial ideals and odd holes in graphs (with C. Francisco and H.T. Ha)
    Journal of Algebraic Combinatorics 32 (2010) 287-301.
  56. A conjecture on critical graphs and connections to the persistence of associated primes. (with C. Francisco and H.T. Ha)
    Discrete Mathematics 310 (2010) 2176-2182.
  57. Algebraic properties of the path ideal of a tree (with J. He)
    Communications in Algebra 38 (2010) 1725-1742.
  58. Simplicial complexes and Macaulay's inverse systems (with F. Zanello)
    Mathematische Zeitschrift 265 (2010) 151-160.
  59. Sequentially Cohen-Macaulay bipartite graphs: vertex decomposability and regularity
    Archiv der Mathematik 93 (2009) 451-459.
  60. Zero-nonzero patterns for nilpotent matrices over finite fields (with K.N. Vander Meulen)
    The Electronic Journal of Linear Algebra 18 (2009) 628-648.
  61. Splittings of monomial ideals (with C. Francisco and H.T. Ha)
    Proceedings American Mathematical Society 137 (2009) 3271-3282.
  62. Shellable graphs and sequentially Cohen-Macaulay bipartite graphs (with R. Villarreal)
    Journal of Combinatorial Theory, Series A 115 (2008) 799-814.
  63. ACM sets of points in multiprojective space (with E. Guardo)
    Collectanea Mathematica 59 (2008) 191-213.
  64. Separators of points in a multiprojective space (with E. Guardo)
    Manuscripta Mathematica 126 (2008) 99-113.
  65. Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers (with H.T. Ha)
    Journal of Algebraic Combinatorics 27 (2008) 215-245.
  66. Resolutions of square-free monomial ideals via facet ideals: a survey (with H.T. Ha)
    Contemporary Mathematics. 448 (2007) 91-117.
  67. Some families of componentwise linear monomial ideals (with C. Francisco)
    Nagoya Mathematical Journal 187 (2007) 115-156.
  68. The minimal resolutions of double points in P1 x P1 with ACM support (with E. Guardo)
    J. Pure Appl. Algebra 211 (2007) 784-800.
    See the CoCoA and Macaulay 2 code for the algorithm in this paper.
  69. Sequentially Cohen-Macaulay Edge Ideals (with C. Francisco)
    Proceedings American Mathematical Society 135 (2007) 2327-2337.
  70. On the linear strand of an edge ideal (with M. Roth)
    Communications in Algebra 35 (2007) 821-832.
  71. Splittable ideals and the resolutions of monomial ideals (with H.T. Ha)
    Journal of Algebra 309 (2007) 405-425.
  72. Multigraded regularity: coarsenings and resolutions (with J. Sidman, H. Wang).
    Journal of Algebra 301 (2006) 703-727.
  73. Multigraded regularity: syzygies and fat points (with J. Sidman).
    Beitrage zur Algebra und Geometrie 47 (2006) 67-87.
    Note: Due to a mixup, the wrong version ended up in the journal;
    the final version can only be found in the journal website.
  74. 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) 257-266.
  75. An appendix to a paper of Catalisano, Geramita, Gimigliano: the Hilbert function of generic sets of 2-fat points in P1 x P1 .
    In Projective Varieties with Unexpected Properties. de Gruyter (2005) 109-112.
  76. Powers of complete intersections: graded Betti numbers and applications (with E. Guardo).
    Illinois J. Math. 49 (2005) 265-279.
  77. On the defining ideal of a set of points in multi-projective space.
    Journal of the London Math. Soc. 72 (2005) 73-90.
  78. Fat points of P1 x P1 and their Hilbert Functions (with E. Guardo).
    Canad. J. Math 56 (2004) 716-741
  79. The regularity of points in multi-projective spaces (with H.T. Ha).
    J. Pure Appl. Algebra 187 (2004) 153-167.
  80. The Hilbert function of ACM set of points in Pn1 x ... x Pnk.
    Journal of Algebra 264 (2003) 420--441.
  81. The border of the Hilbert function of a set of points in Pn1 x ... x Pnk.
    J. Pure Appl. Algebra 176 (2002) 223-247.
  82. Computing the Spreading and Covering Numbers (with E. Carlini, H.T. Ha).
    Communications in Algebra 29 (2001) 5687--5699.
  83. Fat Points on a grid in P2 (with M. Buckles, E. Guardo).
    Matematiche (Catania) 55 (2000), no. 1, 169--189 (2001).
  84. Fat Points on a generic almost complete intersection (with M. Buckles, E. Guardo).
    Matematiche (Catania) 55 (2000), no. 1, 191--202 (2001).
Preprints and Work in Progress

Some of these preprints are avaiblable at Mathematics ArXiv

  1. Conditions for Virtually Cohen--Macaulay Simplicial Complexes (with Jay Yang)
    Preprint (2023).
  2. Three invariants of geometrically vertex decomposable ideals (with Thai Thanh Nguyen, Jenna Rajchgot)
    Preprint (2023).

Software Packages

  1. The GeometricDecomposability package for Macaulay2 (with M. Cummings)
    The Journal of Software for Algebra and Geometry 14 (2024) 41--50.
  2. EdgeIdeals: a package for (hyper)graphs (with C. Francisco and A. Hoefel)
    The Journal of Software for Algebra and Geometry 1 (2009) 1-4.
    Here is the Macaulay 2 code for this package.

Expository Articles

  1. Chromatic numbers via commutative algebra.
    CMS Notes 15 (2019) 14--15.
  2. A Beginner's Guide to Edge and Cover Ideals
    In Monomial Ideals, Computations and Applications
    Lecture Notes in Mathematics Volume 2083, 2013, pp 63-94

Papers in non-refereed journals

  1. 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) 215--221.
  2. 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) 227--237.
  3. 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) 245--262.
  4. 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) 263--273.
  5. The graph and the image of a rational map from Pn to Pm (with H.T. Ha).
    In The Curves Seminar at Queen's, Vol XII, Queen's Papers in Pure and Appl. Math. 114 (1998) 141-162.

Unpublished Papers

  1. The Field of N-Torsion Points of an Elliptic Curve (2001).
    An unpublished paper containing some results of my Master's thesis; this is the final version.

Theses

  1. Sets of Points in Multi-Projective Spaces and their Hilbert Function.
    (2001) Ph.D. thesis, Queen's University. (PDF file)
  2. The Field of N-Torsion points of an Elliptic Curve over a Finite Field.
    (1997) M.Sc. thesis, Queen's University. (PDF file)
  3. 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)

Last Updated: January 26, 2024
URL: http://ms.mcmaster.ca/~vantuyl/papers.html