Selected Publications

(* denotes undergraduate coauthor)

  1. Summation Formulas, Generating Functions, and Polynomial Division, Mathematics Magazine, 95 (2022), no. 5, 509-519 (with M. Brilleslyper).
  2. The corner poset with an application to an n-dimensional hypercube stacking puzzle, Australasian Journal of Combinatorics 84 (2022), vol. 1, 86-110 (with J. Schettler).
  3. Subgraphs of coprime graphs on sets of consecutive integers, Integers 22 (2022), paper no. A47, 18 pages (with M. Brilleslyper).
  4. Shortest paths in the Sierpinski Carpet and Menger Sponge.  Fractals, 28 (2020), no. 7, Id 2050120-55.  Published online, 23 November (with D. Smith).
  5. The mod 2 cohomology rings of congruence subgroups in the Bianchi groups.”  Journal of Algebraic Combinatorics, 52 (2020), no. 4, 527-560 (with G. Lakeland, and A. Rahm).
  6. Berkove, A. Eickemeyer*, and M. Schulman*. The 4-color cubes puzzle. Integers 18 (2018), paper no. A68, 23 pages.
  7. Automorphisms of S6 and the color cubes puzzle. Australas. J. Combin., 68 (2017), 71 – 93 (with D. Cervantes Nava*, D. Condon*, and R. Katz*).
  8. The color cubes puzzle with two and three colors. In The mathematics of various entertaining subjects. Vol. 2, pages 125 – 140. Princeton Univ. Press, Princeton, NJ, 2017 (with D. Cervantes-Nava*, D. Condon*, A. Eickemeyer*, R. Katz*, and M. Schulman*).
  9. The mod 2 cohomology rings of SL2 of the imaginary quadratic integers, J. Pure Appl. Algebra 220 (2016), no. 3, 944-975 (with A. Rahm).
  10. Service learning in a capstone modeling course, PRIMUS, Volume 23 Number 6 (Special Issue on Service-Learning in Mathematics), 2013, 507 –518.
  11. The cohomology groups of the outer Whitehead automorphism group of a free product, Forum Mathematicum, Vol. 22, 2010, No. 2, 379–395 (with J. Meier).  pdf
  12. An analysis of the (colored cubes)3 puzzle, Discrete Mathematics, Volume 308, Number 7, 2008, 1033–1045 (with J. VanSickle, B. Hummon, and J. Kogut).  pdf  (Here are are two representative Mathematica notebooks that we used during the solution of this problem (change the txt extension to nb):  Notebook 1  Notebook 2 ).
  13. The integral cohomology of the Bianchi groups, Transactions of the American Mathematical Society, Volume 358, Number 3, 2006, 1033–1049.
  14. It’s OK to be square if you’re a flexagon, Mathematics Magazine, 77 (2004), no. 5, 335-348 (with J. Dumont*).
  15. Algebraic K-theory of mapping class groups, K-Theory, 32 (2004), 83-100 (with D. Juan-Pineda, and Q. Lu).
  16. A geometric approach to the lower algebraic K-theory of Fuchsian groups, Topology and its Applications, 119 (2002), 269-277 (with D. Juan-Pineda and K. Pearson).
  17. A mathematical analysis of train routes, PRIMUS, Vol. XII, No 4, 2002, 247–264, (with G. Kobylski and W. Farmer). doc
  18. The lower algebraic K-theory of Fuchsian groups,” Commentarii Mathematici Helvetici 76, (2001), 339-352 (with D. Juan-Pineda, and K. Pearson).
  19. The Farrell-Jones Isomorphism Conjecture for finite co-volume hyperbolic actions and the algebraic K-theory of Bianchi groups, Transactions of the American Mathematical Society, Vol. 352, No. 12, (2000), 5689-5702 (with T. Farrell, D. Juan-Pineda, and K. Pearson).
  20. On the mod 2 cohomology of the Bianchi groups, Transactions of the American Mathematical Society, Vol. 352, No. 10, (2000), 4585-4602.
  21. The long arm of calculus, The College Mathematics Journal, 29 (1998), no. 5, 376-387 (with R. Marchand).
  22. On the K-theory of Bianchi groups, Boletín de la Sociedad Matemática Mexicana (3) Vol. 2, (1996), 15-29 (with D. Juan-Pineda).

Code for the 4-Color Cubes Puzzle  

Please reach out to me if you’d like a copy of one of these publications