Research:

Publications:

1. (with L. Traldi) "Tied Dice".  Journal of Combinatorial Mathematics and Combinatorial Computing, 68 (2009) 85-96.

   • Click for a preprint or the supplemental n = 4 case

2. "Monomial graphs and generalized quadrangles".  Finite Fields and Their Applications, 18 (2012) 674-684.

   The article directly from the journal A preprint of the article Supplement on binomial coefficient congruences was published in the Journal of Integer Sequences; see publication #5 below.

3.   (with F. Lazebnik) "When can you factor a quadratic form?"  Mathematics Magazine 87 (2014) 25-37.

   • Directly from the journal, or a draft (May 2013)

4. Entries in the Online Encyclopedia of Integer Sequences

   • A247984 Constant terms of congruences derived from a permutation polynomial motivated by generalized quadrangles.  (September 2014)

   • A246800 Even index terms of A247984, a sequence motivated by generalized quadrangles. (November 2014)

5. "An Integer Sequence Motivated by Generalized Quadrangles".  Journal of Integer Sequences, 18 (2015) no. 7, Article 15.7.8, 13 pp.

   1. Article is freely available to anyone directly from the journal.

6. (with W.H.T. Wong) "Free Flow on a Torus."  Math Horizons, 23 (2016), no. 3, 2.

7. (with F. Lazebnik) "On the uniqueness of some girth eight algebraically defined graphs."  Discrete Applied Mathematics 206 (2016), 188-194.

   • Directly from the journal

8. (with W.H.T. Wong) "Paired many-to-many disjoint path covers of hypertori.'' Discrete Applied Mathematics 218 (2017), 14-20.

   • Directly from the journal

9. (with F. Lazebnik and J. Williford) "On the uniqueness of some girth eight algebraically defined graphs, Part II."  Discrete Applied Mathematics 254 (2019) 161-170.

   • Directly from the journal

10. (with Jathan Austin and S. Molitoris Miller) "The Settlers of Catanbinatorics."  Mathematics Magazine 92 (2019), issue 3, 187-198.

    • Directly from the journal

11. (with A.J. Ganger, S.N. Golden, and C.A. Lyons) "On the girth of two-dimensional real algebraically defined graphs."  Discrete Mathematics 342 (2019) 2834--2842.

    • Directly from the journal

    • This project was supported by NSF #1560222, REU Site: Undergraduate Research in Mathematics, Applied Mathematics, and Statistics at Lafayette College.

12. (with A. Kodess, D. Manzano-Ruiz, and E. Noe) "Classification by girth of three-dimensional algebraically defined monomial graphs over the real numbers.'' Discrete Mathematics 344 (2021).

    • Directly from the journal

13. (with J. Austin and S. Molitoris Miller) "Off to a good start: Using mathematics to evaluate settlement locations in Catan." Book Chapter in Teaching Mathematics Through Games, edited by M. Capaldi. MAA Press: An Imprint of the American Mathematical Society, 2021.

    • From the publisher

14. (with  A. Kodess and  W.H.T. Wong)  "On the Girth of Three-Dimensional Algebraically Defined Graphs with Multiplicatively Separable Functions."  The Electronic Journal of Combinatorics  Volume 29, Issue 4 (2022).   

• Directly from the journal

15. (with E. Donovan, J. Rychtar, D. Tayor, L. Wiglesworth, and W.H.T. Wong)  "Mentoring Students Virtually in Undergraduate Research.'' Book Chapter in Expanding Undergraduate Research in Mathematics: Making UR More Inclusive, edited by M. Dorff, J. Rychtar, and D. Taylor. MAA Press. 2023.

16. (with J. Austin, S. Molitoris Miller, and J. Miller) "Caught "Red"-Handed? The Probability of Randomly Constructing a Legal Catan Board" College Mathematics Journal 54 (2023), issue 4, 187--198.

    • From the publisher

17. (with J. Miller, A. Nash, J. Roeder, H. Samamah and W.H.T. Wong) "Nonisomorphic two-dimensional algebraically defined graphs over R." Journal of Graph Theory (2024), 1--15.

    • From the publisher

Doctoral Dissertation:

"On Polynomial Graphs and Generalize​d Quadrangle​s".  University of Delaware.  May 2013.

Other Documents:

1. Some notes on properties of arcs and ovals in the classical projective plane, culminating with a proof of Segre’s Theorem.  (Last updated October 2012)

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