University of West Florida

Mathematics & Statistics

 

Faculty

Placeholder ImageJaromy S. Kuhl
Associate Professor and Chair

Office Phone: 850-473-7702
E-mail: jkuhl@uwf.edu

11000 University Parkway
Building 4, Room 327
Pensacola, FL 32514

 

 

Courses (Fall 2012)

  • MAS5145: Matrix Theory, MW 6:00-7:15PM
  • 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 Squares

    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;

  • When is a partial latin square completable? (i.e. Given a partial latin square P of order n, is there a latin square of order n for which P can be embedded into?)
  • Are partial latin squares avoidable simultaneously. (i.e. Is there a latin square of order n that contains no part of a given set of partial latin squares of order n.)
  • 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. S. & Denley, T. On avoiding odd partial latin squares and r-multi latin squares. Discrete Mathematics. 306 (2006) 2968-2975.

    Kuhl, J. S. & Denley, T. On a generalization of the Evans conjecture. Discrete Mathematics. 308 (2008) 4763-4767.

    Kuhl, J.S. & Denley, T. Some partial latin cubes and their completions. European Journal of Combinatorics. 32 (2011) 1345-1352.

    Kuhl, J.S. & Denley, T. Constrained Completions of Partial Latin Squares. Discrete Mathematics. 312 (2012) 1252-1256.

    Kuhl, J.S. & Denley, T. A few remarkds on avoiding parital latin squares. Ars Combinatoria. 106 (2012) 313-319.

    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. Math-JK-071912-2.

    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?

     


    Curriculum Vitae

    Office Hours

    • MW: 3:00 - 5:00PM
    • And by Appointment

    Education

    • Ph.D. Mathematics 2005
    • M.S. Mathematics 2003
    • B.S. Mathematics 2001
    • B.A. Physics 2001

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    Mathematics & Statistics | Bldg. 4 | 11000 University Pkwy. | Pensacola, FL 32514 | (850) 474-2276 | Campus Map | Text Only