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

(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

(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

(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

(with Roberto Pelayo)

American Mathematical Monthly

**122**(2015), no. 2, 121-137. [doi] [arXiv:1405.1714]
Teaching publications

The fundamental theorem of finite fields: a proof from first principles

(with Anastasia Chavez)

to appear, American Mathematical Monthly. [arXiv:2010.09124]

(with Anastasia Chavez)

to appear, American Mathematical Monthly. [arXiv:2010.09124]

Discovery learning in an interdisciplinary course on finite fields and applications

(with Lily Silverstein)

to appear, Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS). [arXiv:1810.10568]

(with Lily Silverstein)

to appear, Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS). [arXiv:1810.10568]

Peer-reviewed research publications (* indicates an undergraduate coauthor)

On length densities

(with Scott Chapman and Vadim Ponomarenko)

to appear, Forum Mathematicum. [arXiv:2008.06725]

(with Scott Chapman and Vadim Ponomarenko)

to appear, Forum Mathematicum. [arXiv:2008.06725]

Numerical semigroups, polyhedra, and posets I: the group cone

(with Nathan Kaplan)

to appear, Combinatorial Theory. [arXiv:1912.03741]

(with Nathan Kaplan)

to appear, Combinatorial Theory. [arXiv:1912.03741]

On atomic density of numerical semigroup algebras

(with Ranthony A.C. Edmonds, Bethany Kubik, and Shannon Talbott)

to appear, Journal of Commutative Algebra. [arXiv:2003.01710]

(with Ranthony A.C. Edmonds, Bethany Kubik, and Shannon Talbott)

to appear, Journal of Commutative Algebra. [arXiv:2003.01710]

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)

to appear, Journal of the Australian Mathematical Society. [arXiv:2006.00121]

(with Stephan R. Garcia, Mohamed Omar, and *Timothy Wesley)

to appear, Journal of the Australian Mathematical Society. [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)

to appear, Advances in Geometry. [doi] [arXiv:1912.04460]

(with Jackson Autry, *Abigail Ezell, *Tara Gomes, *Christopher Preuss, *Tarang Saluja, and *Eduardo Torres Davila)

to appear, Advances in Geometry. [doi] [arXiv:1912.04460]

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

(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

(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

(with Jackson Autry, *Tara Gomes, and Vadim Ponomarenko)

American Mathematical Monthly

**127**(2020), no. 8, 744-749. [arXiv:1908.06448]
The elasticity of Puiseux monoids

(with Felix Gotti)

Journal of Commutative Algebra

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

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

(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

(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

(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

(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

(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

(with *Jacob Hartzer)

Integers

**17**(2017), #A38. [paper] [arXiv:1606.00376]
On factorization invariants and Hilbert functions

Journal of Pure and Applied Algebra

Journal of Pure and Applied Algebra

**221**(2017), no. 12, 3069-3088. [doi] [arXiv:1503.08351]
Mesoprimary decomposition of binomial submodules

Journal of Algebra

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

(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

(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

(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

(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

(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

(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

(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

(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

On minimal presentations of shifted affine semigroups with low embedding dimension

(with Isabel White)

Involve

(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

(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)

Length density and numerical semigroups

(with *Cole Brower, Scott Chapman, *Travis Kulhanek, *Joseph McDonough, *Vody Pavlyuk, and Vadim Ponomarenko)

[arXiv:2110.10618]

(with *Cole Brower, Scott Chapman, *Travis Kulhanek, *Joseph McDonough, *Vody Pavlyuk, and Vadim Ponomarenko)

[arXiv:2110.10618]

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)

[arXiv:2108.06063]

(with Stephan R. Garcia and *Gabe Udell)

[arXiv:2108.06063]

Numerical semigroups, polyhedra, and posets III: minimal presentations and face dimension

(with Tara Gomes and *Eduardo Torres Davila)

[arXiv:2009.05921]

(with Tara Gomes and *Eduardo Torres Davila)

[arXiv:2009.05921]