Jaromy S. Kuhl
Office Phone: 850-473-7702
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.
A 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 r-multi latin squares. The following articles contain some of my work in the area of completing and avoiding partial latin squares, latin cubes, and r-multi latin squares.
Kuhl, J. & Hinojosa, H. Avoiding partial latin squares simultaneously. To appear in Graphs and Combinatorics.
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 r-multi latin squares.
4. Let L be a latin square of order qn. Can the rows and columns of L be partitioned into q-sets 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?