Contact
cdoneill «at» sdsu.edu
GMCS Building, Room 570
5500 Campanile Dr
San Diego, CA 92182
U.S.A.
GMCS Building, Room 570
Math & Stats Department
San Diego State University5500 Campanile Dr
San Diego, CA 92182
U.S.A.
Research
My research lies in the intersection of commutative algebra, discrete optimization, and semigroup theory, using methods from algebraic and enumerative combinatorics.
The primary objects of study are combinatorial invariants arising in discrete geometry, with connections to computation, algorithms, and the development and use of software in mathematical research.
As a graduate student at Duke University, I worked under Ezra Miller on combinatorial commutative algebra questions related to mesoprimary decomposition of binomial ideals.
After assisting Scott Chapman, Roberto Pelayo, and Vadim Ponomarenko at various summer research programs, I now study problems in semigroup theory and discrete optimization.
Recently, I have contributed to several interesting projects in algebraic statistics, stemming from the 2016 Mathematics Research Communities on the topic.
In my undergraduate studies at San Fransicso State University, I worked with Matthias Beck in Ehrhart theory and lattice point enumeration, and with Federico Ardila in the study of matroids.
See my complete research statement and annotated publication list for more detail.
Expository and survey publications
Distances between factorizations in the Chicken McNugget monoid
(with Scott Chapman and Pedro García-Sánchez)
College Mathematics Journal 52 (2021), no. 3, 158-176. [doi] [arXiv:1912.04494]
(with Scott Chapman and Pedro García-Sánchez)
College Mathematics Journal 52 (2021), no. 3, 158-176. [doi] [arXiv:1912.04494]
Beyond coins, stamps, and Chicken McNuggets: an invitation to numerical semigroups
(with Scott Chapman and Rebecca Garcia)
A Project-Based Guide to Undergraduate Research in Mathematics (ed. P. Harris, E. Insko, A. Wootton)
Foundations of Undergraduate Research in Mathematics Series, Birkhäuser, Cham. [doi] [arXiv:1902.05848]
(with Scott Chapman and Rebecca Garcia)
A Project-Based Guide to Undergraduate Research in Mathematics (ed. P. Harris, E. Insko, A. Wootton)
Foundations of Undergraduate Research in Mathematics Series, Birkhäuser, Cham. [doi] [arXiv:1902.05848]
Factoring in the Chicken McNugget monoid
(with Scott Chapman)
Mathematics Magazine 91 (2018), no. 5, 323-336. [doi] [arXiv:1709.01606]
(with Scott Chapman)
Mathematics Magazine 91 (2018), no. 5, 323-336. [doi] [arXiv:1709.01606]
Factorization invariants in numerical monoids
(with Roberto Pelayo)
Algebraic and Geometric Methods in Discrete Mathematics (ed. H. Harrington, M. Omar, M. Wright)
Contemporary Mathematics 685 (2017), 231-249. [doi] [arXiv:1508.00128]
(with Roberto Pelayo)
Algebraic and Geometric Methods in Discrete Mathematics (ed. H. Harrington, M. Omar, M. Wright)
Contemporary Mathematics 685 (2017), 231-249. [doi] [arXiv:1508.00128]
How do you measure primality?
(with Roberto Pelayo)
American Mathematical Monthly 122 (2015), no. 2, 121-137. [doi] [arXiv:1405.1714]
(with Roberto Pelayo)
American Mathematical Monthly 122 (2015), no. 2, 121-137. [doi] [arXiv:1405.1714]
Teaching publications
Discovery learning in an interdisciplinary course on finite fields and applications
(with Lily Silverstein)
Problems, Resources, and Issues in Mathematics Undergraduate Studies 33 (2023), no. 4, 355-370. [doi] [arXiv:1810.10568]
(with Lily Silverstein)
Problems, Resources, and Issues in Mathematics Undergraduate Studies 33 (2023), no. 4, 355-370. [doi] [arXiv:1810.10568]
The fundamental theorem of finite fields: a proof from first principles
(with Anastasia Chavez)
American Mathematical Monthly 129 (2022), no. 3, 268-275. [doi] [arXiv:2010.09124]
(with Anastasia Chavez)
American Mathematical Monthly 129 (2022), no. 3, 268-275. [doi] [arXiv:2010.09124]
Peer-reviewed research publications (* indicates an undergraduate coauthor)
Graver bases of shifted numerical semigroups with 3 generators
(with James Howard)
[arXiv:2212.02373] to appear, Journal of Algebra and its Applications.
(with James Howard)
[arXiv:2212.02373] to appear, Journal of Algebra and its Applications.
On the cardinality of minimal presentations of numerical semigroups
(with *Ceyhun Elmacioglu, Kieran Hilmer, *Hannah Koufmann, and *Melin Okandan)
to appear, Algebraic Combinatorics. [arXiv:2211.16283]
(with *Ceyhun Elmacioglu, Kieran Hilmer, *Hannah Koufmann, and *Melin Okandan)
to appear, Algebraic Combinatorics. [arXiv:2211.16283]
When is a numerical semigroup a quotient?
(with Tristram Bogart and Kevin Woods)
Bulletin of the Australian Mathematical Society 109 (2024), no. 1, 67-76. [doi] [arXiv:2212.08285]
(with Tristram Bogart and Kevin Woods)
Bulletin of the Australian Mathematical Society 109 (2024), no. 1, 67-76. [doi] [arXiv:2212.08285]
Convexity in (colored) affine semigroups
(with Jesus De Loera and Chengyang Wang)
Studia Scientiarum Mathematicarum Hungarica 60 (2023), no. 2-3, 143-158. [doi] [arXiv:2212.02452]
(with Jesus De Loera and Chengyang Wang)
Studia Scientiarum Mathematicarum Hungarica 60 (2023), no. 2-3, 143-158. [doi] [arXiv:2212.02452]
Enumerating numerical sets associated to a numerical semigroup
(with *April Chen, Nathan Kaplan, *Liam Lawson, and *Deepesh Singhal)
Discrete Applied Mathematics 341 (2023), 218-231. [doi] [arXiv:2211.17090]
(with *April Chen, Nathan Kaplan, *Liam Lawson, and *Deepesh Singhal)
Discrete Applied Mathematics 341 (2023), 218-231. [doi] [arXiv:2211.17090]
Numerical semigroups, polyhedra, and posets III: minimal presentations and face dimension
(with Tara Gomes and *Eduardo Torres Davila)
Electronic Journal of Combinatorics 30 (2023), no. 2, #P2.57. [doi] [arXiv:2009.05921]
(with Tara Gomes and *Eduardo Torres Davila)
Electronic Journal of Combinatorics 30 (2023), no. 2, #P2.57. [doi] [arXiv:2009.05921]
Length density and numerical semigroups
(with *Cole Brower, Scott Chapman, *Travis Kulhanek, *Joseph McDonough, *Vody Pavlyuk, and Vadim Ponomarenko)
CANT 2021 Proceedings (Combinatorial and Additive Number Theory V), 79-98. [doi] [arXiv:2110.10618]
(with *Cole Brower, Scott Chapman, *Travis Kulhanek, *Joseph McDonough, *Vody Pavlyuk, and Vadim Ponomarenko)
CANT 2021 Proceedings (Combinatorial and Additive Number Theory V), 79-98. [doi] [arXiv:2110.10618]
On length densities
(with Scott Chapman and Vadim Ponomarenko)
Forum Mathematicum 34 (2022), no. 2, 293-306. [doi] [arXiv:2008.06725]
(with Scott Chapman and Vadim Ponomarenko)
Forum Mathematicum 34 (2022), no. 2, 293-306. [doi] [arXiv:2008.06725]
On atomic density of numerical semigroup algebras
(with Ranthony A.C. Edmonds, Bethany Kubik, and Shannon Talbott)
Journal of Commutative Algebra 14 (2022), no. 4, 455-470. [doi] [arXiv:2003.01710]
(with Ranthony A.C. Edmonds, Bethany Kubik, and Shannon Talbott)
Journal of Commutative Algebra 14 (2022), no. 4, 455-470. [doi] [arXiv:2003.01710]
Factorization length distribution for affine semigroups IV: a geometric approach to weighted factorization lengths in three-generator numerical semigroups
(with Stephan R. Garcia and *Gabe Udell)
Communications in Algebra 50 (2022), no. 8, 3481-3497. [doi] [arXiv:2108.06063]
(with Stephan R. Garcia and *Gabe Udell)
Communications in Algebra 50 (2022), no. 8, 3481-3497. [doi] [arXiv:2108.06063]
Factorization length distribution for affine semigroups III: modular equidistribution for numerical semigroups with arbitrarily many generators
(with Stephan R. Garcia, Mohamed Omar, and *Timothy Wesley)
Journal of the Australian Mathematical Society 113 (2022), no. 1, 21-35. [doi] [arXiv:2006.00121]
(with Stephan R. Garcia, Mohamed Omar, and *Timothy Wesley)
Journal of the Australian Mathematical Society 113 (2022), no. 1, 21-35. [doi] [arXiv:2006.00121]
Numerical semigroups, polyhedra, and posets II: locating certain families of semigroups
(with Jackson Autry, *Abigail Ezell, *Tara Gomes, *Christopher Preuss, *Tarang Saluja, and *Eduardo Torres Davila)
Advances in Geometry 22 (2022), no. 1, 33-48. [doi] [arXiv:1912.04460]
(with Jackson Autry, *Abigail Ezell, *Tara Gomes, *Christopher Preuss, *Tarang Saluja, and *Eduardo Torres Davila)
Advances in Geometry 22 (2022), no. 1, 33-48. [doi] [arXiv:1912.04460]
Numerical semigroups, polyhedra, and posets I: the group cone
(with Nathan Kaplan)
Combinatorial Theory 1 (2021), #19. [doi] [arXiv:1912.03741]
(with Nathan Kaplan)
Combinatorial Theory 1 (2021), #19. [doi] [arXiv:1912.03741]
Factorization length distribution for affine semigroups II: asymptotic behavior for numerical semigroups with arbitrarily many generators
(with Stephan R. Garcia, Mohamed Omar, and *Samuel Yih)
Journal of Combinatorial Theory, Series A 178 (2021), 105358. [doi] [arXiv:1911.04575]
(with Stephan R. Garcia, Mohamed Omar, and *Samuel Yih)
Journal of Combinatorial Theory, Series A 178 (2021), 105358. [doi] [arXiv:1911.04575]
Weighted means of B-splines, positivity of divided differences, and complete homogeneous symmetric polynomials
(with Albrecht Böttcher, Stephan R. Garcia, and Mohamed Omar)
Linear Algebra and its Applications 608 (2021), 68-83. [doi] [arXiv:2001.01658]
(with Albrecht Böttcher, Stephan R. Garcia, and Mohamed Omar)
Linear Algebra and its Applications 608 (2021), 68-83. [doi] [arXiv:2001.01658]
Elasticity in Apéry sets
(with Jackson Autry, *Tara Gomes, and Vadim Ponomarenko)
American Mathematical Monthly 127 (2020), no. 8, 744-749. [doi] [arXiv:1908.06448]
(with Jackson Autry, *Tara Gomes, and Vadim Ponomarenko)
American Mathematical Monthly 127 (2020), no. 8, 744-749. [doi] [arXiv:1908.06448]
The elasticity of Puiseux monoids
(with Felix Gotti)
Journal of Commutative Algebra 12 (2020), no. 3, 319-331. [doi] [arXiv:1703.04207]
(with Felix Gotti)
Journal of Commutative Algebra 12 (2020), no. 3, 319-331. [doi] [arXiv:1703.04207]
On parametrized families of numerical semigroups
(with *Franklin Kerstetter)
Communications in Algebra 48 (2020), no. 11, 4698-4717. [doi] [arXiv:1909.04281]
(with *Franklin Kerstetter)
Communications in Algebra 48 (2020), no. 11, 4698-4717. [doi] [arXiv:1909.04281]
Sequentially embeddable graphs
(with Jackson Autry)
Journal of Graph Theory 95 (2020), no. 1, 27-33. [doi] [arXiv:1812.02904]
(with Jackson Autry)
Journal of Graph Theory 95 (2020), no. 1, 27-33. [doi] [arXiv:1812.02904]
Wilf's conjecture in fixed multiplicity
(with Winfried Bruns, Pedro García-Sánchez, and Dane Wilbourne)
International Journal of Algebra and Computation 30 (2020), no. 4, 861-882. [doi] [arXiv:1903.04342]
(with Winfried Bruns, Pedro García-Sánchez, and Dane Wilbourne)
International Journal of Algebra and Computation 30 (2020), no. 4, 861-882. [doi] [arXiv:1903.04342]
A computer algebra system for R: Macaulay2 and the m2r package
(with David Kahle and Jeff Sommars)
Journal of Statistical Software 93 (2020), no. 9, 1-31. [doi] [arXiv:1706.07797]
(with David Kahle and Jeff Sommars)
Journal of Statistical Software 93 (2020), no. 9, 1-31. [doi] [arXiv:1706.07797]
The geometry and combinatorics of discrete line segment hypergraphs
(with Deborah Oliveros and Shira Zerbib)
Discrete Mathematics 343 (2020), no. 6, 111825. [doi] [arXiv:1807.04826]
(with Deborah Oliveros and Shira Zerbib)
Discrete Mathematics 343 (2020), no. 6, 111825. [doi] [arXiv:1807.04826]
A sequence of quasipolynomials arising from random numerical semigroups
(with *Calvin Leng)
Journal of Integer Sequences 22 (2019), no. 6, Art. 19.6.2. [paper] [arXiv:1809.09915]
(with *Calvin Leng)
Journal of Integer Sequences 22 (2019), no. 6, Art. 19.6.2. [paper] [arXiv:1809.09915]
Augmented Hilbert series of numerical semigroups
(with *Jeske Glenn, Vadim Ponomarenko, and *Benjamin Sepanski)
Integers 19 (2019), #A32. [paper] [arXiv:1806.11148]
(with *Jeske Glenn, Vadim Ponomarenko, and *Benjamin Sepanski)
Integers 19 (2019), #A32. [paper] [arXiv:1806.11148]
Factorization length distribution for affine semigroups I: numerical semigroups with three generators
(with Stephan R. Garcia and *Samuel Yih)
European Journal of Combinatorics 78 (2019), 190-204. [doi] [arXiv:1804.05135]
(with Stephan R. Garcia and *Samuel Yih)
European Journal of Combinatorics 78 (2019), 190-204. [doi] [arXiv:1804.05135]
On arithmetical numerical monoids with some generators omitted
(with *Sung Hyup Lee and *Brandon Van Over)
Semigroup Forum 98 (2019), no. 2, 315-326. [doi] [arXiv:1712.06741]
(with *Sung Hyup Lee and *Brandon Van Over)
Semigroup Forum 98 (2019), no. 2, 315-326. [doi] [arXiv:1712.06741]
Some algebraic aspects of mesoprimary decomposition
(with Laura Matusevich)
Journal of Pure and Applied Algebra 223 (2019), no. 1, 380-394. [doi] [arXiv:1706.07496]
(with Laura Matusevich)
Journal of Pure and Applied Algebra 223 (2019), no. 1, 380-394. [doi] [arXiv:1706.07496]
On the computation of factorization invariants for affine semigroups
(with Pedro García-Sánchez and *Gautam Webb)
Journal of Algebra and its Applications 18 (2019), no. 1, 1950019, 21 pp. [doi] [arXiv:1504.02998]
(with Pedro García-Sánchez and *Gautam Webb)
Journal of Algebra and its Applications 18 (2019), no. 1, 1950019, 21 pp. [doi] [arXiv:1504.02998]
On mesoprimary decomposition of monoid congruences
Rocky Mountain Journal of Mathematics 48 (2018), no. 6, 2069-2085. [doi] [arXiv:1708.03441]
Rocky Mountain Journal of Mathematics 48 (2018), no. 6, 2069-2085. [doi] [arXiv:1708.03441]
Random numerical semigroups and a simplicial complex of irreducible semigroups
(with Jesus De Loera and Dane Wilbourne)
Electronic Journal of Combinatorics 25 (2018), no. 4, #P4.37. [paper] [arXiv:1710.00979]
(with Jesus De Loera and Dane Wilbourne)
Electronic Journal of Combinatorics 25 (2018), no. 4, #P4.37. [paper] [arXiv:1710.00979]
Realizable sets of catenary degrees of numerical monoids
(with Roberto Pelayo)
Bulletin of the Australian Mathematical Society 97 (2018), no. 2, 240-245. [doi] [arXiv:1705.04276]
(with Roberto Pelayo)
Bulletin of the Australian Mathematical Society 97 (2018), no. 2, 240-245. [doi] [arXiv:1705.04276]
Apéry sets of shifted numerical monoids
(with Roberto Pelayo)
Advances in Applied Mathematics 97 (2018), 27-35. [doi] [arXiv:1708.09527]
(with Roberto Pelayo)
Advances in Applied Mathematics 97 (2018), 27-35. [doi] [arXiv:1708.09527]
Minimal presentations of shifted numerical monoids
(with *Rebecca Conaway, Felix Gotti, *Jesse Horton, Roberto Pelayo, *Mesa Pracht, and Brian Wissman)
International Journal of Algebra and Computation 28 (2018), no. 1, 53-68. [doi] [arXiv:1701.08555]
(with *Rebecca Conaway, Felix Gotti, *Jesse Horton, Roberto Pelayo, *Mesa Pracht, and Brian Wissman)
International Journal of Algebra and Computation 28 (2018), no. 1, 53-68. [doi] [arXiv:1701.08555]
Unimodular hierarchical models and their Graver bases
(with Daniel Bernstein)
Journal of Algebraic Statistics 8 (2017), no. 2, 29-43. [doi] [arXiv:1704.09018]
(with Daniel Bernstein)
Journal of Algebraic Statistics 8 (2017), no. 2, 29-43. [doi] [arXiv:1704.09018]
On the periodicity of irreducible elements in arithmetical congruence monoids
(with *Jacob Hartzer)
Integers 17 (2017), #A38. [paper] [arXiv:1606.00376]
(with *Jacob Hartzer)
Integers 17 (2017), #A38. [paper] [arXiv:1606.00376]
On factorization invariants and Hilbert functions
Journal of Pure and Applied Algebra 221 (2017), no. 12, 3069-3088. [doi] [arXiv:1503.08351]
Journal of Pure and Applied Algebra 221 (2017), no. 12, 3069-3088. [doi] [arXiv:1503.08351]
Mesoprimary decomposition of binomial submodules
Journal of Algebra 480 (2017), 59-78. [doi] [arXiv:1511.00161]
Journal of Algebra 480 (2017), 59-78. [doi] [arXiv:1511.00161]
Sparse solutions of linear Diophantine equations
(with Iskander Aliev Jesus De Loera, and Timm Oertel)
SIAM Journal on Applied Algebra and Geometry 1 (2017), no. 1, 239-253. [doi] [arXiv:1602.00344]
(with Iskander Aliev Jesus De Loera, and Timm Oertel)
SIAM Journal on Applied Algebra and Geometry 1 (2017), no. 1, 239-253. [doi] [arXiv:1602.00344]
On dynamic algorithms for factorization invariants in numerical monoids
(with *Thomas Barron and Roberto Pelayo)
Mathematics of Computation 86 (2017), 2429-2447. [doi] [arXiv:1507.07435]
(with *Thomas Barron and Roberto Pelayo)
Mathematics of Computation 86 (2017), 2429-2447. [doi] [arXiv:1507.07435]
On the set of elasticities in numerical monoids
(with *Thomas Barron and Roberto Pelayo)
Semigroup Forum 94 (2017), no. 1, 37-50. [doi] [arXiv:1409.3425]
(with *Thomas Barron and Roberto Pelayo)
Semigroup Forum 94 (2017), no. 1, 37-50. [doi] [arXiv:1409.3425]
Irreducible decomposition of binomial ideals
(with Thomas Kahle and Ezra Miller)
Compositio Mathematica 152 (2016), 1319-1332. [doi] [arXiv:1503.02607]
(with Thomas Kahle and Ezra Miller)
Compositio Mathematica 152 (2016), 1319-1332. [doi] [arXiv:1503.02607]
On the set of catenary degrees of finitely generated cancellative commutative monoids
(with Vadim Ponomarenko, *Reuben Tate, and *Gautam Webb)
International Journal of Algebra and Computation 26 (2016), no. 3, 565-576. [doi] [arXiv:1506.07587]
(with Vadim Ponomarenko, *Reuben Tate, and *Gautam Webb)
International Journal of Algebra and Computation 26 (2016), no. 3, 565-576. [doi] [arXiv:1506.07587]
Numerical semigroups on compound sequences
(with Vadim Ponomarenko and *Claire Kiers)
Communications in Algebra 44 (2016), no. 9, 3842-3852. [doi] [arXiv:1503.05993]
(with Vadim Ponomarenko and *Claire Kiers)
Communications in Algebra 44 (2016), no. 9, 3842-3852. [doi] [arXiv:1503.05993]
Factorization properties of Leamer monoids
(with *Jason Haarmann, *Ashlee Kalauli, *Aleesha Moran, and Roberto Pelayo)
Semigroup Forum 89 (2014), no. 2, 409-421. [doi] [arXiv:1309.7477]
(with *Jason Haarmann, *Ashlee Kalauli, *Aleesha Moran, and Roberto Pelayo)
Semigroup Forum 89 (2014), no. 2, 409-421. [doi] [arXiv:1309.7477]
On the linearity of ω-primality in numerical monoids
(with Roberto Pelayo)
Journal of Pure and Applied Algebra 218 (2014), no. 9, 1620-1627. [doi] [arXiv:1309.7476]
(with Roberto Pelayo)
Journal of Pure and Applied Algebra 218 (2014), no. 9, 1620-1627. [doi] [arXiv:1309.7476]
Monoid congruences, binomial ideals, and their decompositions
Doctoral dissertation, Duke University (2014).
Doctoral dissertation, Duke University (2014).
Student journal publications
Counting edges in factorization graphs of numerical semigroup elements
(with Mariah Moschetti)
submitted, Involve. [arXiv:2401.06912]
(with Mariah Moschetti)
submitted, Involve. [arXiv:2401.06912]
On minimal presentations of shifted affine semigroups with low embedding dimension
(with Isabel White)
Involve 14 (2021), no. 4, 617-630. [doi] [arXiv:2006.01396]
(with Isabel White)
Involve 14 (2021), no. 4, 617-630. [doi] [arXiv:2006.01396]
Squarefree divisor complexes of certain numerical semigroup elements
(with *Jackson Autry, *Paige Graves, *Jessie Loucks, Vadim Ponomarenko, and *Samuel Yih)
Involve 14 (2021), no. 1, 1-9. [doi] [arXiv:1804.06632]
(with *Jackson Autry, *Paige Graves, *Jessie Loucks, Vadim Ponomarenko, and *Samuel Yih)
Involve 14 (2021), no. 1, 1-9. [doi] [arXiv:1804.06632]
Preprints (submitted)
Numerical semigroups, polyhedra, and posets IV: walking the faces of the Kunz cone
(with *Cole Brower and Joseph McDonough)
[arXiv:2401.06025]
(with *Cole Brower and Joseph McDonough)
[arXiv:2401.06025]
The structure theorem for sets of length for numerical semigroups
(with *Gilad Moskowitz)
[arXiv:2311.05786]
(with *Gilad Moskowitz)
[arXiv:2311.05786]
Atomic density of arithmetical congruence monoids
(with *Nils Olsson and Derek Rawling)
[arXiv:2310.07924]
(with *Nils Olsson and Derek Rawling)
[arXiv:2310.07924]
Minimal free resolutions of numerical semigroup algebras via Apéry specialization
(with Benjamin Braun, Tara Gomes, Ezra Miller, and Aleksandra Sobieska)
[arXiv:2310.03612]
(with Benjamin Braun, Tara Gomes, Ezra Miller, and Aleksandra Sobieska)
[arXiv:2310.03612]
On faces of the Kunz cone and the numerical semigroups within them
(with *Levi Borevitz, Tara Gomes, *Jiajie Ma, *Harper Niergarth, *Daniel Pocklington, *Rosa Stolk, *Jessica Wang, and *Shuhang Xue)
[arXiv:2309.07793]
(with *Levi Borevitz, Tara Gomes, *Jiajie Ma, *Harper Niergarth, *Daniel Pocklington, *Rosa Stolk, *Jessica Wang, and *Shuhang Xue)
[arXiv:2309.07793]
Numerical semigroups via projections and via quotients
(with Tristram Bogart and Kevin Woods)
[arXiv:2306.11564]
(with Tristram Bogart and Kevin Woods)
[arXiv:2306.11564]