Research

For student research, click here.

Research Interests

Finite Geometries, combinatorics, and other topics in discrete mathematics and geometry.

Publications

• 1. With N. Abarzua & R. Pomareda. Feet in Orthogonal-Buekenhout-Metz Unitals. Advances in Geometry 18 (2018), Issue 2, Pages 229–236. pdf.

  2. With W. Cherowitzo & N. L. Johnson. α-flokki and partial α-flokki. Innovations in Incidence Geometry 15 (2017), 5–29. pdf.

  3. With J. Elder. A Note on the Factorization of Permutations into Cycles. International Electronic Journal of Algebra 22 (2017), 125-132. pdf.

  4. With R. Adams, J. Dixon, J. Elder, J. Peabody & K. Willis. Combinatorial Analysis of a Subtraction Game on Graphs. International Journal of Combinatorics vol. 2016, Article ID 1476359, 8 pages. pdf.

  5. With J. Hauschild & J. Ortiz. On the Levi Graph of Point-Line Configurations. Involve, a Journal of Mathematics 8 (2015), no. 5, 893-900. pdf.

  6. With K. Mellinger & R. Vaughn. Graphs Embedded into Finite Projective Planes. Contributions to Discrete Mathematics 10 (2015), no. 1, 113-125. pdf.

  7. With I. Birnbaum, R. McDonald, M. Kuneli & K. Urabe. The well-covered dimension of products of graphs. Discussiones Mathematicae Graph Theory 34 (2014), no. 4, 811-827. pdf.

  8. With E. Aceves, D. Heywood & A. Klahr. Cycles in Projective Spaces. Journal of Geometry 105 (2014), no. 1, 111-117. pdf.

  9. With J. Peabody & J. White. Cycles, wheels, and gears in finite planes. Contributions to Discrete Mathematics 8 (2013), no. 2, 75-87. pdf.

  10. With F. Lazebnik & K. Mellinger. Embedding cycles in finite planes. The Electronic Journal of Combinatorics 20 (2013), no. 3, Paper 24, 17 pp. pdf

  11. With L. Cusick. Finite groups of derangements on the n-cube II. The Electronic Journal of Combinatorics 18 (2011), no 1, Paper 196, 6 pp. pdf

  12. With E. Diaz. Translation planes admitting a linear Abelian group of order (q+1)². Note di Matematica 29 (2009), suppl. 1, 59-68. pdf.

  13. With F. Lazebnik & K. Mellinger. On the number of k-gons in finite projective planes. Note di Matematica 29 (2009), suppl. 1, 135-151. pdf.

  14. Geometric structures arising from generalized j-planes. Note di Matematica 29 (2009), no. 2, 1-19. pdf.

  15. Generalized j-planes. Note di Matematica 29 (2009), no. 2, 143-164. pdf

  16. With N. L. Johnson. Symplectic spreads and symplectically paired spreads. Note di Matematica 26 (2006), no. 2, 119-135. pdf

  17. With N. L. Johnson & F. W. Wilke. j,k-planes of order 4³. Innovations in Incidence Geometry 2 (2005), 1-34. pdf.

• • (In progress) With R. Pomareda. Unitals in Figueroa planes.

  • (In progress) With R. Pomareda. An algebraic invariant for spreads.

  • (Stalled) With V. Jha & N. L. Johnson. Large autotopism groups and flat flocks.

  • (Stalled) with E. Diaz. Translation planes admitting a group of order (q+1)².

Books

• • With T. Forgacs. Analysis and Algebra. ISBN: 978-1-935551-64-5. 2013.

  • With R. Amarasinghe, L. Burger, M. Nogin, & A. Tuska. Exploring Mathematics: Investigations for Elementary School Teachers. ISBN: 978-1-62131-058-7. 2013.

  • With R. Amarasinghe & K. Premadasa. Advanced Algebra for Teachers. ISBN: 978-1-93555-157-7. 2013.

• With M. Cordero & A. Montinaro, Editors. Proceedings of NormFest. ISSN: 1123-2536. e-ISSN: 1590-0932. 2009.

Selected Talks

• • Coloring graphs and commuting graph of groups: Fresno State Summer REU's Colloquium. California State University, Fresno. July 31st, 2018. pdf

  • Unitales en los planos de Figueroa (In Spanish): Santiago Number Theory and Algebra Seminar (SaNTAS). Departmento de Matematicas. Facultad de Ciencias, Universidad de Chile. April 4th, 2018. pdf

  • Figueroa planes and the unitals they (may) contain: Department of Mathematics Seminar. California State University, Fresno. February 9th, 2018. pdf

  • Unitals in Figueroa planes: AMS/MAA Joint Mathematics Meetings. San Diego, CA. January 11th, 2018. pdf

  • NSF-Funded Intensive Summer Research Experiences for Undergraduates (REUs) in Mathematics: 2017 CSU STEM Conference. LAX Crowne Plaza. August 11th, 2017. pdf

  • El Teorema de Futurama (In Spanish): Coloquio de Matematicas. Departmento de Matematicas. Facultad de Ciencias, Universidad de Chile. March 23rd, 2016. pdf

  • The Well-Covered Dimension of Generalized Quadrangles: AMS/MAA joint meeting. Seattle, WA. January 9th, 2016. pdf

  • Feet in Buekenhout-Metz Unitals: Fall AMS Western Sectional Meeting. California State University, Fullerton. October 24th, 2015. pdf

  • α-flokki: AMS/MAA joint meeting. San Antonio, TX. January 12th, 2015. pdf

  • Embedding Graphs into Finite Projective Planes and Spaces: Rocky Mountain Algebraic Combinatorics Seminar. Colorado State University. October 25th, 2013. pdf

  • Undergraduate Research on Discrete Mathematics at Fresno State: Discrete Mathematics Seminar. University of Colorado Denver. October 25th, 2013. pdf

  • Embedding Graphs into Finite Projective Planes: Discrete Mathematics Seminar. University of Delaware. October 10th, 2013. pdf

  • Pancyclicity in finite projective planes: AMS/MAA joint meeting. San Diego, CA. January 12th, 2013. pdf

  • Autotopism groups and jj...j-planes: AMS/MAA joint meeting. Boston, MA. January 5th, 2012. pdf

  • Groups of derangements of the n-cube: AMS Spring Central Sectional Meeting. Iowa City, IA. March 20th, 2011. pdf

Editorial work, refereeing, and reviewing. I adhere to this manifesto

• • PUMP Journal of Undergraduate Research. Managing Editor.

  • Math Reviews (MathSciNet). Reviewer.

  • Note di Matematica. Referee.

  • The Electronic Journal of Combinatorics. Referee.

• Algebraic Combinatorics. Referee.

  • Graphs and Combinatorics. Referee.

  • Linear and Multilinear Algebra. Referee.

  • Pensamiento Educativo. Referee.

My Erdös number is less or equal to 3.

- P. Erdös and Z. Füredi. Families of finite sets in which no set is covered by the union of two others. J. Combin. Theory Ser. A 33 (1982), no. 2, 158-166.

- F. Lazebnik and Z. Füredi. Graphs of prescribed girth and bi-degree. J. Combin. Theory Ser. B 64 (1995), no. 2, 228-239.

- F. Lazebnik, K. Mellinger, and O. Vega. Embedding cycles in finite planes. The Electronic Journal of Combinatorics 20(3) #24. 2013.

or

- N. Alon and P. Erdös. Disjoint edges in geometric graphs. Discrete Comput. Geom. 4 (1989), no. 4, 287-290.

- N. Alon, K. Mellinger, D. Mubayi, J. Verstraëte. The de Bruijn-Erdös theorem for hypergraphs. Des. Codes Cryptogr. 65 (2012), no. 3, 233-245.

- F. Lazebnik, K. Mellinger, and O. Vega. Embedding cycles in finite planes. The Electronic Journal of Combinatorics 20(3) #24. 2013.

My math genealogy is here.

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