### Publications

1. James Hammer, Joshua Harrington, and Lenny Jones. On the congruence $x^x \equiv x \pmod{n}$. Integers, 16:Paper No. A74, 17, 2016

2. John Asplund, Joe Chaffee, and James M. Hammer. Some bounds on the size of DI-pathological graphs. J. Combin. Math. Combin. Comput., 99:107–129, 2016

3. John Asplund, Joe Chaffee, and James M. Hammer. Decomposition of a complete bipartite multigraph into arbitrary cycle sizes. Graphs and Combinatorics, 33(4):715–728, 2017

4. James Hammer and Dean Hoffman. Factor pair Latin squares. Australas. J. Combin., 69:41–57, 2017

5. Kelly B. Guest, James M. Hammer, Peter D. Johnson, and Kenneth Roblee. Regular clique assemblies, configurations, and friendship in edge-regular graphs. Tamkang J. Math., 48(4):301–320, 2017

6. Braxton Carrigan and James Hammer. Traveling in networks with blinking node. Theory Appl. Graphs, 5(1):Art. 2, 2018

7. John Asplund, Joe Chaffee, James Hammer, and Matt Noble. $\gamma’$-Realizability and Other Musings on Inverse Domination. Theory and Applications of Graphs, 5(1):Art 5, 7, 2018.

8. James Hammer and John Lorch. Orthogonal factor-pair latin squares of prim-power order. Journal of Combinatorial Designs, 27(9):552-561, 2019.

9. Graph Polynomials for a Class of DI-Pathological Graphs, joint work with Joshua Harrington. Accepted in AKCE International Journal of Graphs and Combinatorics.

10. Odd Coverings of Subsets of the Integers, joint work with Joshua Harrington and Kristina Marotta. Accepted to the Journal of Combinatorics and Number Theory Volume 10 Issue 2.

### Articles Submitted or In Preparation

1. Sudoku Pair Latin Squares, joint work with Braxton Carrigan, David Diaz, and Robert Lorch. Submitted.

2. H-Decompositions of Generalized Johnson Graphs, joint work with Braxton Carrigan and Aaron Clark. Submitted.

3. On the domination Number of Permutation Graphs and an Application to Strong Fixed Points, joint work with T. Baren, M. Cory, M. Friedberg, P. Gardner, J. Hammer, J. Harrington, D. McGinnis, R. Waechter, and T. W. H. Wong. ArXiv:1810.03409. Submitted.

4. A Regional Kronecker Product and Sudoku-Pair Latin Squares, joint work with Braxton Carrigan and John Lorch. Submitted.

### OEIS Contributions

1. Makkah Davis, James Hammer, Bob Kuo, Jordan Lenchitz, Leah S. Miller, and Boyang Su. A289849, August 2017. Cardinality of the maximal set of ordered factor pairs such that a Quasi-Factor Pair Latin Square of order n exists.

2. Makkah Davis, James Hammer, Bob Kuo, Jordan Lenchitz, Leah S. Miller, and Boyang Su. A289812, August 2017. n for which a Factor Pair Latin Square of order n exists.

3. N. J. A. Sloane. A006932, October 2018. Addition Exact Formula to: Number of permutations of [n] with at least one strong fixed point (a permutation p of {1,2,…,n} is said to have j as a strong fixed point if $p(k) < j$ for $k < j$ and $p(k) > j$ for $k > j$).

4. Daniel A. McGinnis & James Hammer. A320578, October 2018. Triangle read by rows: $T(n,k)$ is the number of permutation graphs on n vertices with domination number k, with $1 \leq k \leq n$.

5. Daniel A. McGinnis & James Hammer. A320579, October 2018. Triangle read by rows: $T(n,k)$ is the number of disconnected permutation graphs on n vertices with domination number k, with $2 \leq k \leq n$.

6. Daniel A. McGinnis & James Hammer. A320583, October 2018. Triangle read by rows: $T(n,k)$ is the number of connected permutation graphs on n vertices with domination number k, with $1 \leq k \leq \left\lfloor \frac{n}{2} \right\rfloor$.