Research

Xavier's primary research interests reside in the areas of linear algebra, spectral graph theory and combinatorics. Below is a list of his research papers, as well as a list of talks delivered and posters presented.

 
Peer-Reviewed Journal Publications

Submitted

  1. S. M. Fallat, X. Martínez-Rivera, On the almost-principal minors of a symmetric matrix, submitted. [arXiv:1807.07448].
  2. A. Abiad, B. Brimkov, X. Martínez-Rivera, S. O, J. Zhang, Spectral bounds for the connectivity of regular graphs with given order, submitted. [arXiv:1703.02748].
Published/in press/to appear

  1. S. M. Fallat, X. Martínez-Rivera, The quasi principal rank characteristic sequence, Linear Algebra and its Applications 548 (2018), 42-56. [arXiv:1711.01003], [DOI:10.1016/j.laa.2018.02.024].
  2. X. Martínez-Rivera, The signed enhanced principal rank characteristic sequence, Linear and Multilinear Algebra 66(7) (2018), 1484-1503. [arXiv:1612.08940], [DOI:10.1080/03081087.2017.1363149].
  3. A. Abiad, B. Brimkov, A. Erey, L. Leshock, X. Martínez-Rivera, S. O, S.-Y. Song, J. Williford, On the Wiener index, distance cospectrality and transmission regular graphs, Discrete Applied Mathematics 230 (2017), 1-10. [arXiv:1609.06911], [DOI:10.1016/j.dam.2017.07.010].
  4. X. Martínez-Rivera, The enhanced principal rank characteristic sequence over a field of characteristic 2, Electronic Journal of Linear Algebra 32 (2017), 273-290. [DOI:10.13001/1081-3810.3389].
  5. S. Butler, M. Catral, H. T. Hall, L. Hogben, X. Martínez-Rivera, B. Shader, P. van den Driessche, The enhanced principal rank characteristic sequence for Hermitian matrices, Electronic Journal of Linear Algebra 32 (2017), 58-75. [DOI:10.13001/1081-3810.3249].
  6. X. Martínez-Rivera, Classification of families of pr- and epr-sequences,
    Linear and Multilinear Algebra 65(8) (2017), 1581-1599. [arXiv:1606.07495], [DOI:10.1080/03081087.2016.1248345].
  7. M. Archer, M. Catral, C. Erickson, R. Haber, L. Hogben, X. Martínez-Rivera, A. Ochoa, Potentially eventually exponentially positive sign patterns ,
    Involve 6(3) (2013), 261-271. [DOI:10.2140/involve.2013.6.261].
  8. M. Archer, M. Catral, C. Erickson, R. Haber, L. Hogben, X. Martínez-Rivera, A. Ochoa, Constructions of potentially eventually positive sign patterns with reducible positive part , Involve 4(4) (2011), 405-410. [DOI:10.2140/involve.2011.4.405].





Technical Reports

  1. M. Muñoz-Figueroa, X. Martínez-Rivera, T. Seaquist, B. Crawford, A. Mubayi, K. Salau, C. Kribs-Zaleta. Two strain competition: Trypanosoma cruzi. Written at the Mathematical and Theoretical Biology Institute (MTBI) REU (2009). [mtbi.asu.edu/2009-7].



Talks and Posters

Invited talks

  1. 2017 - Dec., The epr-sequence over a field of characteristic 2, Matrix Theory Seminar, Georgia State University, Atlanta, GA, USA.

  2. 2017 - July, The signed epr-sequence, 21st Conference of the International Linear Algebra Society (Mini-symposium on Combinatorial Matrix Theory), Iowa State University, Ames, IA, USA.

  3. 2017 - July, The sepr-sequence of a Hermitian matrix, Special Western Canada Linear Algebra Meeting (WCLAM), Banff International Research Station (BIRS), Banff, Alberta, Canada.

  4. 2017 - June, Principal rank characteristic sequences, Linear Algebra Seminar, Auburn University, Auburn, AL, USA.

  5. 2016 - Oct., The epr-sequence over a field of characteristic 2, AMS Fall Central Sectional Meeting (Special Session on Combinatorial Matrix Theory), University of St. Thomas–Minnesota, Minneapolis, MN, USA.

  6. 2016 - April, Classification of families of pr- and epr-sequences, AMS Spring Central Sectional Meeting (Special Session on Matrix and Operator Theory), North Dakota State University, Fargo, ND, USA.

  7. 2016 - March, Classification of families of pr- and epr-sequences, 47th Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC) (Special Session on Combinatorial Matrix Theory, in honor of LeRoy Beasley), Florida Atlantic University, Boca Raton, FL, USA.

Contributed talks

  1. 2018 - May, The qpr-sequence, Western Canada Linear Algebra Meeting (WCLAM), Washington State University, Pullman, WA, USA.

  2. 2018 - March, The quasi principal rank characteristic sequence, XXXIII Seminario Interuniversitario de Investigación en Ciencias Matemáticas (SIDIM), University of Puerto Rico–Río Piedras, San Juan, PR, USA.

  3. 2017 - March, The signed enhanced principal rank characteristic sequence, XXXII Seminario Interuniversitario de Investigación en Ciencias Matemáticas (SIDIM), University of Puerto Rico–Ponce, Ponce, PR, USA.

  4. 2017 - Jan., The epr-sequence over a field of characteristic 2, 2017 Joint Mathematics Meetings, Atlanta, GA, USA.

  5. 2016 - July, Classification of families of pr- and epr-sequences, 20th Conference of the International Linear Algebra Society, Katholieke Universiteit Leuven, Leuven, Belgium.

  6. 2016 - May, Classification of families of pr- and epr-sequences, Western Canada Linear Algebra Meeting (WCLAM), University of Manitoba, Winnipeg, Manitoba, Canada.

  7. 2015 - Oct., The principal rank characteristic sequence and the enhanced principal rank characteristic sequence, SIAM Conference on Applied Linear Algebra, Atlanta, GA, USA.

  8. 2012 - July, Classification of potentially eventually exponentially positive sign patterns of small order, 2012 SIAM Annual Meeting, Minneapolis, MN, USA.

Departmental talks

  1. 2015 - Oct., The principal rank characteristic sequence and the enhanced principal rank characteristic sequence, SIAM ISU Student Chapter, Iowa State University, Ames, IA, USA.

  2. 2017 - Sept., A new principal rank characteristic sequence, Linear Algebra Seminar, Auburn University, Auburn, AL, USA.

Posters presented (as an undergraduate)

  1. 2010 - Oct., (Joint with Rana Haber) Classification of potentially eventually exponentially positive sign patterns of small order, 2010 SACNAS National Conference, Anaheim, CA, USA.

  2. 2010 - Feb., Two strain competition: Trypanosoma cruzi, NEA Science Day, University of Puerto Rico–Mayagüez, Mayagüez, PR, USA.

  3. 2009 - Oct., Two strain competition: Trypanosoma cruzi, 2009 SACNAS National Conference, Dallas, TX, USA.

  4. 2009 - Sept., Two strain competition: Trypanosoma cruzi, Ana G. Méndez University System (AGMUS) XX Undergraduate Research Symposium, San Juan, PR, USA.