ISU Combinatorial Matrix Research Group

summer 2011


        This is a group of faculty and students who are interested in combinatorial matrix theory, with some or all of the research taking place at ISU.    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 published 20 papers with more 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), which will be offered in spring 2014, 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

  • People   

    Current

    Former members longterm members (many were Leslie Hogben's students or postdocs)

    Papers

    1. The P_0-Matrix Completion Problem (2000-1)
    Choi, DeAlba, Hogben, Maxwell, Wangsness.

        Electronic Journal of Linear Algebra 9 (2002): 1-20

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

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

    4. 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 ]

    5. 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.

    6. 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.
     
    7. 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 ]

    8. 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.

    9. 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.

    10. 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.

    11. 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]

    12. 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]

    13. 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]

    14. 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

    15. Potentially eventually exponentially positive sign patterns  (2010 REU)
    Archer, Catral, Erickson, Haber, Hogben, Martinez-Rivera, Ochoa.  Involve 6 (2013): 261-271.

    16. Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees.   (2011 EGR)
    Ekstrand, Erickson,  Hay, Hogben, Roat. Electonic Journal of Linear Algebra 23 (2012) 79-87 [PDF preprint]

    17. Positive semidefinite zero forcing number.   (2011 EGR)
     Ekstrand, Erickson,  Hall, Hay, Johnson, Kingsley, Osborne, Peters, Roat, Ross, Row, Warnberg, Young.    Linear Algebra and its Applications, 439 (2013): 1862 – 1874. [PDF preprint]

    18. Computing Positive Semidefinite Minimum Rank for Small Graphs..   (2011 EGR)
     
    Osborne and Warnberg.  To appear in Involve.

    19. Propagation time for zero forcing on a graph.  (2011 REU)
    Hogben, Huynh, Meyer, Kingsley, Walker, Young. 
    Discrete Applied Mathematics, 160 (2012) 1994-2005.. [PDF preprint]

    20. Zero forcing number, maximum nullity, and path cover number of subdivided graphs.  (2011 REU)
    Catral, Cepek, Hogben, Huynh,  Lazebnik,  Peters, 
    Young Electronic Journal of Linear Algebra, 23 (2012), 906-922 [PDF]

    21. Minimum rank, maximum nullity, and zero forcing number for simple digraphs. (2011)
    A. Berliner, M. Catral, L. Hogben, M. Huynh, K. Lied, M. Young.  .
     
    [PDF]

    22. Minimum rank with zero diagonal.    (2012 REUF)
    C. Grood, J. Harmse, L. Hogben, T. Hunter, B. Jacob, A. Klimas, S. McCathern.  To appear in
    Electronic Journal of Linear Algebra  [PDF]

    24. Path cover number, maximum nullity, and zero forcing number of oriented graphs and other simple digraphs.  (2013 REU) Adam Berliner, Cora Brown, Joshua Carlson, Nathanael Cox, Leslie Hogben, Jason Hu, Katrina Jacobs, Kathryn Manternach, Travis Peters, Nathan Warnberg, Michael Young.  To appear in Involve.
    [PDF]

    25.
    Minimum rank of graphs with loops.  C. Bozeman, AV. Ellsworth, L. Hogben, J.C.-H. Lin, G. Maurer, K. Nowak, A. Rodriguez, J. Strickland. Electron. J. Linear Algebra  27 (2014):  907 – 934. [PDF]

    REU 2013


    REUF2012 meeting at ISU during summer 2013


    summer 2010
    The research group summer
     
    Leslie Hogben's Homepage Nov 18, 2016