Research

I'm primarily interested in combinatorics, especially considering connections with commutative algebra and simplicial topology, as well as recreational mathematics associated with games or sports.

Publications:

1. Generalized splittings of monomial ideals with R. Bouchat, to appear, International Elec. J. Algebra.

2. Using words to enumerate and construct maximum  nonattacking chessboard arrangements, to appear, Applied Mathematical Analysis and Computation - 1st SGMS, Statesboro, GA, U.S., April 2-3, 2021 (Virtual), edited by D. Wanduku.

3. Becoming a More Effective Instructor Using Primary Source Projects, to appear, Math. Enthusiast.

4. Lattice Path Coronoids, Open J. Discrete Appl. Math 6(3) (2023) 1-21.

5. Nonattacking Arrangements of Kings on Even Length Chessboard, Mathematica Notebook Archive (2022).

6. Multigraded Betti numbers of Mobius domino ideals, Communications in Algebra 50(5) (2022) 2269-2278. https://doi.org/10.1080/00927872.2021.2005078.

7. "A Three-Part Module on Poverty", Mathematics and Social Justice: Focusing on Quantitative Reasoning and Statistics, MAA Press, Classroom Resource Materials 66 (2021), edited by G. Karaali & L. Khadjavi.

8. "Why do we choose to do what we do? Using statistics to investigate our actions,'' Mathematical Themes in a First-Year Seminar, MAA Press (2021), edited by J. Bowen, M. Kozek, P. Pierce, & J. Schaefer.

9. Queens, Attack!, Math. Intelligencer 42 (2020) 65-73. https://doi.org/10.1007/s00283-019-09963-y

10. Exploring mod 2 n-queens games, with A. Ladha, Recreat. Math. Mag. 11 (2019) 15-25.

11. The Problem of Pawns, Elec. J. Comb. 22(3) (2019) Article P3.21.

12. On the unimodality of convolutions of sequences of binomial coefficients, J. Integer Seq. 22 (2019) Article 19.2.8.

13. Fibonacci numbers and resolutions of domino ideals, with R. Bouchat, J. Algebra Comb. Discrete Struct. Appl. 6(2) (2019) 63-74.

14. Introductory Mathematics and Statistics through Sports: Supplementary Activities and Writing Projects, with E. Kahn, Oxford University Press (June 2019).

15. Minimal free resolutions of 2 x n domino tilings, with R. Bouchat, J. Algebra Appl. 18(6) (2019), 1950118 (16 pages).

16. On the enumeration of k-omino towers, Discrete Math. 340 (2017), 1319-1326

17. Convex Domino Towers, J. Integer Seq. 20(3), (2017), 1-18.

18. A constructive approach to the minimal free resolutions of path ideals of trees, with R. Bouchat, J. Algebra Comb. Discrete Struct. Appl. 4(1), (2017), 1-13.

19. Multi-graded Betti numbers of path ideals of trees, with R. Bouchat, J. Algebra Appl. 16(1), (2017), 1-20.

20. Kaleidoscopes, Chessboards, and Symmetry, J. Humanistic Math. 6(1), (2016), 110-126.

21. A professional development framework for the flipped classroom model: Design and implementation of a literacy and math integrated professional development initiative, with A. Katz and J. Kim, Handbook of Research on Active Learning and the Flipped Classroom Model in the Digital Age, IGI Global (2016), edited by J. Keengwe and G. Onchwari, 122--149.

22. Exploring Discrete Mathematics with American Football, with E. Kahn, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies 25(5), (2015), 421-438.

23. Nonattacking arrangments of n-queens with initial placements, Journal of Recreational Mathematics 38(2), (2014), 23-37.

24. The Rees product of posets, with M. Readdy, Journal of Combinatorics 2(2), (2011), 165-191.

25. How deep is your playbook? with E. Kahn, Mathematics and Sports, The Mathematical Association of America (2010), edited by J. A. Gallian.

26. The Rees product of the cubical lattice with the chain, with M. Readdy, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'08), 571-582, Discrete Math. Theoret. Comput. Sci. Proc., AJ, Assoc. Discrete Math. Theor. Comput. Sci, Nancy, (2008).

Integer Sequences:

• New sequence entries: A275204, A275599, A275662 

• Contributions to existing sequences: A117468 

Preprints:

1. Losing Matters: A European Association Football Model for NCAA Men's Basketball with E. Kahn.

2. Maximum arrangements of nonattacking kings on the 2n x 2n chessboard.