Michael Fraboni

Publications

• Cram with Polyominoes with Emma Miller. Appears in The Mathematics Exchange 17.1 (2023), pp. 39-48.

• The Birank Number of 3 × n Grid Graphs with Shane Harder. Appears in The Mathematics Exchange 11.1 (2017), pp. 1–13.

• The Birank Number of Operationally Constructed Graphs with Andrew Benson in Congr. Numer. 228 (2017), pp. 17–22 .

• The birank number of ladder, prism and Möbius ladder graphs with Madison Zebrine while she was a student here at Moravian College.  Appears in the Australasian journal of Combinatorics, Volume 63(1) (2015), 34–40.

• The birank number of a graph with Michael Fisher at WCUPA and Darren Narayan at Rochester Institute of Technology in Congr. Numer. 204 (2010), 173-180.

• Maximum graphs with unique minimum dominating set of size two with Nathan Shank here at Moravian College in the Australasian journal of Combinatorics, Volume 46 (2010), 91–99.

• Strong q-Convexity in Uniform Neighborhoods of Subvarieties in Coverings of Complex Spaces a joint paper with Terrence Napier from Lehigh University which appeard in Mathematische Zeitschrift volume 265 (2010), no. 3, 653-685.

• Fractals in the Classroom a joint paper with Trisha Moller in Mathematics Teacher, volume 102, no. 3 (October 2008).

• Culture Points: Engaging students outside the classroom a joint paper with Kevin Hartshorn from Moravian College which appeared in PRiMUS, Volume XVII(2) (2007), pages 117-124.

• q-Convexity Properties of Coverings of Complex Manifolds appeared in Mathematische Zeitschrift, Volume 254 (2006), no. 3, 553-566

• Conjugacy and the 3x+1 Conjecture My paper about the 3x+1 problem (also known as the Collatz Conjecture). It was written as an undergraduate research project at the University of Scranton with Ken Monks.

Student Work

• On the Expansion of Common Combinatorial Games by Emma Miller.  Emma completed her honors project in the spring of 2022.

• Upper Bounds on the Birank Number of G3,n by Shane Harder. Shane completed his honors project in the spring of 2016.

• Birank Number of Operationally Constructed Graphs by Andrew Benson. Andrew completed this honors project in the spring of 2013.

• The Collatz Conjecture: A Conjugacy Approach by James T Long III. I advised Jamie in his honors project which he completed in December of 2008. In addition, he presented a chapter of his thesis at the 2008 Midstates Conference on Undergraduate Research in Mathematics and Computer Science where it is published in the conference proceedings.

• Explorations of the Collatz Conjecture by Kelly Latourette. I advised Kelly in her honors project which she completed in December of 2007.