Faculty 

Jaromy S. Kuhl Office Phone: 8504737702 11000 University Parkway


Courses (Fall 2012)
Research Interests: Combinatorics  Design and Graph Theory.Major Interests: Latin Squares and Bipartite Graphs, Hamiltonicity and Longest Cycles, Tutte Polynomial, Graph Colorings, and Competition Graphs and Competition Numbers. Latin SquaresA partial latin square of order n is an nxn arrangment of n symbols in which each symbol occurs at most once in each row and column. If each symbol appears in each row and column, then we say the arrangment is a latin square of order n. In my research I try to answer the following kinds of questions; Some common generalizations of the latin square are latin cuboids and rmulti latin squares. The following articles contain some of my work in the area of completing and avoiding partial latin squares, latin cubes, and rmulti latin squares. Kuhl, J. & Hinojosa, H. Avoiding partial latin squares simultaneously. To appear in Graphs and Combinatorics. Kuhl, J. & Hinojosa, H. Unavoidable partial latin squares of order 4. MathJK0719122. Here are some questions/problems about partial latin squares that I would like to answer and maybe there are some UWF math students who would like to help me. 1. If P is partial latin square of order nr and if all nonempty cells in P occur in the rxr subsquares along the main diagonal, can P be completed? 2. Characterize the unavoidable pairs of partial latin squares of small orders. 3. Find long partial transversals in rmulti latin squares. 4. Let L be a latin square of order qn. Can the rows and columns of L be partitioned into qsets such that the induced qxq subsquares of L contain a symbol no more than q/2 times? 5. Can a latin cuboid of order nxnx2 always be extended? 6. Let A be an array of order n on n symbols such that each symbol appears at most n/2 times. Can A be avoided? 
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