Current Research and Publications

Journal Publications

[1] B. Ahmadi, F. Alinaghipour, S. Fallat, Y. Fan, K. Meagher and S. Nasserasr. The minimum rank of universal adjacency matrices. Submitted to Linear Algebra and its Applications. Oct. 2011
available (arXiv).
[2] K. Meagher and A. Purdy. An Erdos-Ko-Rado theorem for multisets. Electronic Journal of Combinatorics 18 (2011), no.1, Paper 220, 8 pp available (arXiv).
[3] R. Bailey, A. Burgess, M. Cavers and K. Meagher. Generalized covering designs and clique coverings. Journal of Combinatorial Designs 19 (2011), 378-406, 2011. 10.1002/jcd.20288 (arXiv).
[4] R. Bailey and K. Meagher. On the metric dimension of Grassman graphs. submited to Discrete Math and Theoretical Computer Science, May 2010.
[5] K. Meagher and P. Spiga. An Erdos-Ko-Rado theorem for the derangement graph of PGL(2,q) acting on the projective line. to appear Journal of Combinatorial Theory Series A. October 2009.
available at www.arxiv.org/pdf/0910.3193.
[6] C. Godsil and K. Meagher. Multiplicity-free representations of the symmetric group, to appear Annals of Combinatorics, 38 pages, 13(4):463-490, 2009.
available at www.arxiv.org/pdf/math.RT/0612567.
[7] C. Godsil and K. Meagher. A new proof of the Erdos-Ko-Rado theorem for intersecting families of permutations. European Journal of Combinatorics, 30(2):404-414, 2009.
available at www.arxiv.org/pdf/0710.2109.
[8] K. Meagher, L. Moura and L. Zekaoui. Mixed covering arrays on graphs. Journal of Combinatorial Designs, 15(5):393-404, 2007.
[9] K. Meagher, L. Moura and B. Stevens. A Sperner-type theorem for set-partition systems, Electronic Journal of Combinatorics, 12(1) Note 20, 6 pp. (electronic), 2005.
[10] K. Meagher and L. Moura. Erdos-Ko-Rado theorems for uniform set-partition systems. Electronic Journal of Combinatorics, 12(1) Research Paper 40, 12 pp. (electronic), 2005.
[11] K. Meagher and B. Stevens. Covering arrays on graphs. Journal of Combinatorial Theory, Series B, 95(1):134-151, 2005.
[12] K. Meagher and B. Stevens. Group construction of covering arrays. Journal of Combinatorial Designs, 13(1):70-77, 2005.

Other Publications

[13] K. Meagher. Covering arrays on graphs: qualitative independence graphs and extremal set-partition theory. Ph.D. thesis, University of Ottawa, 177 pages, Sept. 2005.
available at www.arxiv.org/pdf/math.CO/0701553.
[14] K. Meagher. Group Construction of Covering Arrays --- Part 2. Technical Report, 5 pages, Jan. 2005.
[15] K. Meagher. Convolution estimates with Orlicz spaces. Masters thesis, University of Waterloo, 130 pages, May 1997.

Presentations and Other Projects

Covering Arrays Graphs

  • This is a paper with Brett Stevens that introduces covering arrays on graphs and an interesting family of graphs that can be used to determine the maximal size of a covering array on graph. (abstract),

    Covering Arrays on small edge-critical Graphs

  • This is a table of results of an exhaustive search for the minimal binary covering array for all edge critical graphs with fewer than 12 vertices. (pdf, postscript)

    • Non-Isomorphic Covering Arrays

  • Lists of Non-Isomorphic Covering Arrays (List of Arrays)
  • This is the paper that explains the search algorithm for non-isomorphic arrays csproject.ps, csproject.pdf)

    • Group Construction of Covering Arrays

  • This paper has a new way to construction small strength 2 covering arrays. Many of the arrays in this paper are smaller than the current best known. ( abstract )
  • This is part two of the previous paper. The previous paper used an exhaustive search in the construction, this search is replaced a hill-climbing algorithm. In this paper new bounds for covering arrays on larger alphabets are given. ( PS , PDF )

    • Presentation for Colloque de Science Mathematique du Quebec

  • Covering arrays on Graphs presentation ( PDF)

    • Presentation for 7th Annual GSAED conference

  • What is math research (presentation) ( PDF)

    • Advanced Comprehensive

  • presentation ( PDF)
  • document, "Covering Arrays on Graphs: connections to design theory, extremal combinatorics and algebraic combinatorics" ( PDF, PS)

    • Presentation for LaCIM

  • "Covering Arrays on Graphs and Connections to Extremal Combinatorics " ( PDF)

    • Presentation for Ontario Combinatorics Workshop 2004

  • "Covering Arrays on Product Graphs" ( PDF)

    • Presentation for Combinatorics and Optimization Seminar 2004

  • "Higher Order Erdos-Ko-Rado Theorems" ( PDF)

    • Presentation for GSAED Conference 2005

  • "Extreme Math" ( PDF)

    • Presentation for Ontario Combinatorics Workshop 2005

  • "Eigenvalues of some of my Favourite Graphs" ( PDF)

    • Presentation for the University of Waterloo Algebraic Combinatorics Seminar July 7 2005

  • "Covering Arrays and Covering Arrays on Graphs" ( PDF)

    • Presentation for the Canadian Math Society - Connecting Women in Math, July 21-23 2005

  • "Covering Arrays and Covering Arrays on Graphs" ( PDF)

    • My Ph.D. thesis

  • "Covering Arrays on Graphs: qualitative independence graphs and extremal set partition theory" ( PDF)

    • Presentation for my thesis defense

  • "Covering Arrays on Graphs: qualitative independence graphs and extremal set partition theory" ( PDF)

    • Presentation for Regina

  • "Covering Arrays on Graphs: extremal partition theory and qualitative independence graphs" ( PDF)

    • Presentation for Ottawa

  • "Two Approaches to the Study of Covering Arrays" ( PDF)

    • Presentations for the Canadam Conference

  • "Covering Arrays on Graphs" ( PDF)
  • "Set-Partitions and Association Schemes" ( PDF)

    • Presentations for Discrete Math Day and Ottawa Graph Theory Conference

  • "Applications of Graph Theory to Covering Arrays" ( PDF)
  • "A Mulit-Partite Erdos-Ko-Rado Theorem" ( PDF)

    • Presentations for Canadian Mathematics Socieity Winter Meeting 2008

  • "An Algebraic Approach to Erdos-Ko-Rado Theorems" ( PDF)

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    Last modified: Mon Sep 9 14:55:10 EDT