ISU Combinatorial Matrix Research Group

summer 2011


        This is a group of faculty and students who are interested in combinatorial matrix theory.    At the beginning of a session we begin by discussing the necessary background, such as the use of graphs and digraphs to study matrices and the use of matrices to study (di)graphs, and review recent developments.  We then select a problem and begin active research.  This is a great opportunity for graduate and undergraduate students to become involved in research-- past groups have written 14 papers and two more are under review.  Graduate linear algebra (Math 510) is a prerequisite for graduate students; undergraduate linear algebra (Math 317 or equivalent) is a prerequisite for the summer REU undergraduates and a course in graph theory is helpful.  Post-doctoral associates and faculty at nearby colleges and universities are also welcome.   Students often join at the beginning of spring semester for EGR (Math 610 Early Graduate Research) or at the beginning of the summer for the REU (Research Experiences for Undergraduates) sessions.  The group used to meet starting at the beginning of each academic year.  For more information contact  Leslie Hogben.
 
  • People
  • ISUCMRG Papers


    • summer 2010
    The research group summer

    People   (university is ISU unless otherwise listed)

    Permanent

    Additional current

    Former members who were Leslie Hogben's students or postdocs

    Papers

    The P_0-Matrix Completion Problem (2000-1)
    Choi, DeAlba, Hogben, Maxwell, Wangsness.
        Electronic Journal of Linear Algebra 9 (2002): 1-20

    The Nonnegative P_0-Matrix Completion Problem (2001-2)
    Choi, DeAlba, Hogben, Kivunge, Nordstrom, Shedenhelm
        Electronic Journal of Linear Algebra 10 (2003): 46-59

    The (Weakly) Sign Symmetric P-Matrix Completion Problems (2002-3)
    DeAlba, Hardy, Hogben, Wangsness
    Electronic Journal of Linear Algebra 10 (2003): 257-271  

    On completion problems for various classes of P-matrices (2003 & 2004 REUs)
    Bowers, Evers, Hogben, Shaner, Snider, Wangsness     
    Linear Algebra and Its Applications     413 (2006) 342-354.  [ PDF preprint ]

    Minimum Rank and Maximum Eigenvalue Multiplicity of Symmetric Tree Sign Patterns (2004-5)
    DeAlba, Hardy, Hentzel, Hogben, Wangsness
    Linear Algebra and Its Applications 418 (2006) 389-415 pdf preprint.

    Rational Realization of Maximum Eigenvalue Multiplicity of Symmetric Tree Sign Patterns (2005 REU) Chowdhury, Hogben, Melancon, Mikkelson
    Linear Algebra and Its Applications 418 (2006) 380-393, pdf preprint.
     
    Spectrally Arbitrary Patterns: Reducibility and the 2n Conjecture     (2005-6)
    DeAlba,  Hentzel, Hogben, McDonald, Mikkelson, Pryporova, Shader, Vander Meulen
    Linear Algebra and Its Applications, 423 (2007)  262-276. [PDF preprint ]

    Minimum Rank of a Tree over an Arbitrary Field (2006 REU)
    Chenette, Droms, Hogben, Mikkelson, Pryporova)       Electronic Journal of Linear Algebra 16 (2007): 183-186.

     Universally optimal matrices and field independence of the minimum rank of a graph (2008 EGR) 
    DeAlba, Grout, Hogben, Mikkelson, Rasmussen
    Electronic Journal of Linear Algebra 18 (2009): 403-419.

    Minimum rank of skew-symmetric matrices described by a graph (2008 IMA graduate summer program)
    Allison,  Bodine, DeAlba, Debnath, DeLoss, Garnett, Grout, Hogben,  Im, Kim, Nair, Pryporova, Savage,  Shader, Wangsness.     Linear Algebra and its Applications 432 (2010) 2457–2472.

    Techniques for determining the minimum rank of a small graph (2008 EGR)
    DeLoss, Grout, Hogben, McKay, Smith, Tims
     Linear Algebra and its Applications 432 (2010) 2995–3001. [PDF preprint]

    Minimum rank of certain families of graphs (2009 REU)
    Almodovar, DeLoss, Hogben, Hogenson, Murphy, Peters, Ramirez. Involve: a journal of mathematics 3 (2010): 371-392. [PDF preprint]

    Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph (2009 REU)
    Edholm, Hogben, Huynh, LaGrange, Row.  Linear Algebra and its Applications 436 (2012): 4352–4372 [PDF preprint]

     Constructions of potentially eventually positive sign patterns with reducible positive part  (2010 REU)
    Archer, Catral, Erickson, Haber, Hogben, Martinez-Rivera, Ochoa.   Involve 4 (2011): 405-410.  PDF preprint

    Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees.   (Electonic Journal of Linear Algebra 23 (2012) 79-87 [PDF preprint]

    Positive semidefinite zero forcing number (2011 EGR)
    Ekstrand, Erickson,  Hall, Hay, Hogben, Johnson, Kingsley, Osborne, Peters, Roat, Ross, Row, Warnberg, Young. Under review. [PDF preprint]

    Potentially eventually exponentially positive sign patterns  (2010 REU)
    Archer, Catral, Erickson, Haber, Hogben, Martinez-Rivera, Ochoa.  Under review.

    Propagation time for zero forcing on a graph.  (2011 REU) Leslie Hogben, My Huynh, Sarah Meyer, Nicole Kingsley, Shanise Walker, Michael Young.  To appear in Discrete Applied Mathematics. [PDF preprint]


     
    Leslie Hogben's Homepage April 2012