Publications

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

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

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
 Cited by Ganesamurthy, S.(6KAREM); Paulraja, P.(6KAREM) in Decompositions of complete tripartite graphs into cycles of lengths 3 and 6. Australas. J. Combin. 73 (2019), 220 – 241.

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

Kelly B. Guest, James M. Hammer, Peter D. Johnson, and Kenneth Roblee. Regular clique assemblies, configurations, and friendship in edgeregular graphs. Tamkang J. Math., 48(4):301–320, 2017
 Cited by Kutnar, Klavdija(SVUPRMI); Marušič, Dragan(SVUPRMI); Miklavič, Štefko(SVUPRMI); Šparl, Primož(SVLJUBD) in The classification of 2extendable edgeregular graphs with diameter 2. Electronic J. Combin. 26 (2019), no. 1, Paper 1.16, 14 pp.

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

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.

James Hammer and John Lorch. Orthogonal factorpair latin squares of primpower order. Journal of Combinatorial Designs, 27(9):552561, 2019.

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

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

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

HDecompositions of Generalized Johnson Graphs, joint work with Braxton Carrigan and Aaron Clark. Submitted.

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.

A Regional Kronecker Product and SudokuPair Latin Squares, joint work with Braxton Carrigan and John Lorch. Submitted.
OEIS Contributions

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 QuasiFactor Pair Latin Square of order n exists.

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.

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 $k > j$).

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 $1 \leq k \leq n$.

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 $2 \leq k \leq n$.

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 $1 \leq k \leq \left\lfloor \frac{n}{2} \right\rfloor$.