Kyle Pula > Research

In broad terms, my research focuses on the interplay between algebra and combinatorics. In particular, I study Latin squares and their algebraic equivalent, loops and quasigroups.

Primary Research Interests

• Latin Squares and other types of Combinatorial Designs
• Finite Non-associative Algebra (Loops and Quasigroups)

Peer Reviewed Publications

1. Products of All Elements in a Loop and a Framework for Non-Associative Analogues of the Hall-Paige Conjecture, Electronic Journal of Combinatorics, Volume 16(1). May 2009.
2. Admissible Orders of Jordan Loops, Journal of Combinatorial Designs, Volume 17, Issue 2, pp 103 - 118. March 2009. Joint work with Michael Kinyon and Petr Vojtechovsky.
3. Powers of Elements in Jordan Loops, Commentationes Mathematicae Universitatis Carolinae, Volume 49(2), pp 291-299. 2008.

Research and Expository Talks

1. Recent Developments in Latin Squares.
   MAA Sectional Meeting, Golden, CO. Spring 2009.
2. The Hall-Paige conjecture in non-associative contexts.
   AMS/MAA Joint Meetings, Combinatorics Contributed Paper Session, Washington, D.C. Winter 2009.
3. A generalization of plexes of Latin squares.
   Rocky Mountain Discrete Math Days. Laramie, WY. Summer 2008.
4. Two Problems on Transversals in Multiplication Tables.
   Automated Deduction and its Application to Mathematics. Albuquerque, NM. Summer 2008.
5. Latin squares with no transversals.
   MAA Rocky Mountain Sectional Meeting. Spearfish, SD. Spring 2008.
6. Jordan Loops.
   Loops & Quasigroups 2007. Prague, Czech Republic. Summer 2007.
7. Using Automated Reasoning to Understand Jordan Loops.
   Automated Deduction and its Application to Mathematics. Albuquerque, NM. Summer 2007.
8. Maximal Gallai Multigraphs.
   Rocky Mountain Discrete Math Days. Ft. Collins, CO. Summer 2007.
9. Gallai Multigraphs.
   AMS Western Sectional Meeting: Graph Theory and Combinatorics Special Session. Tucson, AZ. Spring 2007.
10. Edge-Colored Multigraphs Lacking Colorful Triangles.
    MAA Rocky Mountain Sectional Meeting. Pueblo, CO. Spring 2007.