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Research
 

MACS

Rigoberto Flórez

rigo.florez@citadel.edu
Phone: (843) 953.5034

Mail Address

Department of
Mathematics and
Computer Science

The Citadel
171 Moultrie Street
Charleston, SC 29409

 

 

 

 
 

My area of research is Combinatorics; specifically matroids and their connections with Combinatorial Geometry and Graph Theory. I am working on algebraically representable matroids, projective planes, matroids associated to biased graphs, and graphs. I am also interested in elementary number theory.

 

Publications:

  • R. Florez, R. Higuita, and A. Mukherjee, Geometric Interpretations in the Hosoya Triangle of some Fibonacci Identities. Submitted.
  • E. Czabarka, R. Florez, L. Junes, and J. L. Ramirez, Enumerations of Peaks and Valleys on Non-decreasing Dyck Paths. Submitted.
  • R. Florez, H. A. Newman, H. Miranda and D. Narayan, Uniform Edge Betweenness Centrality. Submitted.
  • R. Florez and T. Zaslavsky, The Projective Planarity Question for Matroids of 3-Nets and Biased Graphs. Submitted. A version in ArXiv.
  • R. Florez, R. Higuita, and A. Mukherjee, Star of David and other patterns in the Hosoya-like polynomials triangles. Submitted. A version in ArXiv.
  • R. Florez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial. Submitted. A version in ArXiv.
  • R. Florez and T. Zaslavsky, Biased Graphs. VI. Synthetic Geometry. Submitted. A version in ArXiv.
  • R. Florez, O. Haynes, D. Narayan and A. Strang, Finding the number of shortest paths and edge betweenness centrality in Cartesian products of paths and cycles. Submitted.
  • R. Florez, E. Carter, B. Ek, D. A. Gonzalez, and D. Narayan, Intersecting Geodesics and Centrality Graphs. Submitted
  • R. Florez and A. Mukherjees, Introducing Students to Conjectures, Exploration and Visual Proofs using Experiments in Topology. Submitted.
  • R. Florez, J. Lind, and D. Narayan, Betweenness centrality in organizational Structures. Accepted for publication in Congressus Numerantium.
  • R. Forez, L. Junes, and J. L. Ramirez, Further Results on Paths in a n-Dimensional Cubic Lattice. Accepted for publication in JIS (2017).
  • R. Florez, R. Higuita and A. Mukherjees, Characterization of the Fibonacci GCD property for generalized Fibonacci polynomials. Acepted for publication in INTEGERS (2017). A version in ArXiv.
  • R. Florez D. Narayan, A. Sharma, R. Vargas, and A. Waldron, A Graph Theoretic Analysis of Leverage Centrality. AKCE Int. J. Graphs Comb. 14 (2017), no. 3, 295–306. A version in ArXiv. Free version AKCE
  • R. Florez, and A. Mukherjees, Solving open problems with students as a first research experience. Teaching mathematics and its applications, (10) (2017), 1-7. Non-free version Teaching Mathematics and its Applications
  • R. Florez, R. Lopez, D. Narayan, H. Wickus, and J. Worrell, Towards a Characterization of Graphs with Distinct Betweenness Centrality. The Australasian Journal of Combinatorics, Volume 68 (part 2), 2017. Free version The Australasian Journal of Combinatorics. MR3646041
  • R. Florez D. Narayan, A. Sharma, R. Vargas, and A. Waldron, Leverage centrality of knight’s graphs and Cartesian products of regular graphs and path powers. Involve. A journal of Mathematics. 10.4 (2017), 583-592. MR3630305
  • B. Baker Swart, R. Florez, D. Narayan, and G. Rudolph, Extrema Property of the k-Ranking of Directed Paths and Cycles. AKCE International Journal of Graphs and Combinatorics 2.6 (2016), 1-16. MR3524756. Free version AKCE-Vol13-1 or AKCE-Vol 13-1. A version in ArXiv.
  • R. Florez and D. A. Narayan, Maximizing the number of edges in optimal k-rankings. AKCE International Journal of Graphs and Combinatorics, 12.1 (2015), 1-8. MR3410846. Free Version AKCE-Vol 10-1. A version in ArXiv.
  • E. Czabarka, R. Florez, and L. Junes, A Discrete Convolution on the Generalized Hosoya Triangle. Journal of Integer Sequences, 18.1 (2015), 1-22. MR3303767. Free Version JIS-Vol 18-1
  • E. Czabarka, R. Florez, and L. Junes, Some Enumerations on Non-decreasing Dyck Paths, The Electronics Journal of Combinatorics, 22.1 (2015) 1-22. MR3315445. Free version EJC-Vol 22
  • R. Florez, R. Higuita and L. Junes, 9-modularity and GCD Properties of Generalized Fibonacci Numbers, Integers 14 (2014), 1-14. MR3268585. Free version INT-Vol 14
  • R. Florez, R. Higuita and A. Mukherjees, Alternating sums in the Hosoya polynomial triangle, Journal of Integer Sequences, 17.9 (2014), 1-17. MR3261053. Free Version JIS-Vol 17-9
  • R. Florez, R. Higuita and L. Junes, GCD property of the Generalized Star of David in Generalized Hosoya's Triangle, Journal of Integer Sequences, 17.4 (2014). MR3168688. 1-17. Free Version JIS-Vol 17-4
  • R. Florez and L. Junes, GCD properties in the Hosoya's Triangle.The Fibonacci Quarterly 50.2 (2012). MR2927935. The Fibonacci Quaterly Vol 50.
  • R. Florez and L. Junes, A Relation Between Triangular Numbers and Prime Numbers. Integers 12 (2012), no. 1, 83-96. MR2955583. Free version INT-Vol 11, other version is at INTEGERS.
  • R. Florez and D. A. Narayan, An optimal k-ranking characterization of oriented paths and cycles, Bulletin of the Institute of Combinatorics and Its Applications. 61 (2011) 97-108. MR2724560
  • R. Florez, Harmonic conjugation in harmonic matroids. Discrete Mathematics. 309 (2009), 2365-2372. MR2276967
  • R. Florez and D. Forge, Minimal non-orientable matroids in a projective plane, Journal of Combinatorial Theory Series A. 114 (2007), 175-183. MR2276967
  • R. Florez, Lindstrom's conjecture on a class of algebraically non-representable matroids. European Journal of Combinatorics, 27 (2006), 896-905. MR2226425
  • Florez, Rigoberto, Four studies in the geometry of biased graphs. Thesis (Ph.D.)-State University of New York at Binghamton. 2005. 78 pp. ISBN: 978-0542-19217-3. MR2707450
  • R. Florez and J. Velez, Failure of splitting from module-finite extension rings. Beitrage zur Algebra und Geometrie (contributions to algebra and geometry), 41 (2000), 345-357. MR1801426. Free version Beitr. Algebra Geom. Vol 41
 

Works in Some State of Preparation:

R. Florez, L. Junes and T. Zaslavsky, Complex apollonian spheres (5 pages).

R. Florez, Projective Rectangles. (20 pages).

R. Florez, Representability of Cm in algebraic matroids.

 

Papers Presented:

  • Characterization of the strong divisibility property for generalized Fibonacci polynomials. Carolina Math Seminar, Benedict College, Columbia SC, Nov 3, 2017
  • Projective Rectangles. AMS Fall Central Sectional Meeting University of North Texas, Denton, TX, Sep 9, 2017.
  • GCD Property of Generalized Fibonacci Polynomials and other identities. INTEGERS Conference 2016, University of West Georgia, October 8, 2016.
  • Una relacion entre los caminos de Dyck y los numeros de Fibonacci. Seminario de Redes Complejas y Combinatoria, Universidad Sergio Arboleda (Colombia), August 3, 2016.
  • Algunos Conteos de los caminos no decrecientes de Dyck. ALTENCOA 7-2016,
    Bucaramanga (Colombia), July 21, 2016.
  • Una relacion entre los caminos de Dyck y los numeros de Fibonacci. Universidad de Antioquia (Medellin), seminario institucional, July 18, 2016.
  • Non-decreasing Dyck paths and Fibonacci Numbers. The Combinatorics
    Seminar, Binghamton University, Binghamton NY, June 28, 2016.
  • Exploring Mathematics with Fibonacci Numbers and Hosoyas Triangle. Rochester Institute of Technology (RIT), June 23, 2016.
  • Projective Representation of Non-Representable Matroids (of Biased Graphs). Discrete Seminar, University of South Carolina Feb 12, 2016.
  • Projective Representation of Non-Representable Matroids (of Biased Graphs). Discrete Math Seminar, Texas State University, San Marcos, Nov 20, 2015.
  • Exploring Mathematics with Fibonacci Numbers and Hosoya's Triangle. Sigma XI brown-bag lunch presentation, The Citadel, October 16, 2015.
  • Experiments in Topology. Rochester Institute of Technology (RIT), June 25, 2015.
  • Explorando Matematicas con Relaciones Recursivas de Segundo Orden en Arreglos Triangulares. Foro departamento de Matematicas de Universidad del Valle (Cali). Seminario institutional, May 29, 2015.
  • Topologia Experimental. Universidad Sergio Arboleda (Bogota). Conductor of a workshop, May 23, 2015.
  • Explorando Matematicas en el Triangulo de Hosoya. Universidad de Antioquia (Medellin), seminario institucional, May 21, 2015.
  • Explorando Matematicas en el Triangulo de Hosoya. Seminario Universidad EAFIT (Medellin), May 15, 2015.
  • Some algebraic and geometric properties of Fibonacci polynomials in the Hosoya triangle. American Mathematical Society (AMS) Joint Mathematics Meetings, San Antonio TX, January 11, 2015.
  • Counting Non-Decreasing Dyck Paths. Discrete Seminar, University of South Carolina Nov 21, 2014.
  • A formal Power Series to Count non-decreasing Dyck paths. Colloquium, College of Charleston Sep 5, 2014.
  • Using Fibonacci Numbers to Count Dyck Paths. Sixteenth International Conference on Fibonacci Numbers and Their Applications, July 25, 2014.
  • Topics in the Hosoya's Triangle. Rochester Institute of Technology (RIT), June 25, 2014.
  • Seminario en Mathemática Elemental y Robótica. Universidad Sergio Arboleda (Bogotá). Conductor of a workshop, June 17-19, 2014..
  • Representacion Proyectiva de Matroids no representable (of Biased Graphs). Universidad de Antioquia (Medellin), seminario institucional, June 9, 2014.
  • A Relation Between Triangular Numbers and Prime Numbers. Rochester Institute of Technology (RIT), June 27, 2013.
  • Using Hosoya's Triangle to Count Some Dyck Paths. MAA, Southeastern Section, Winthrop University, March 16, 2013.
  • Representability of frame matroid and lift Matroid in a Projective Plane. Colloquium, College of Charleston Feb 15, 2013.
  • Convolutions on the Geometry of Hosoya's Triangle. American Mathematical Society (AMS) Joint Mathematics Meetings, San Diego CA, January 9, 2013.
  • GCD Properties in Hosoya's Triangle. MAA Southeastern Section
    Spring 2012 Meeting, Clayton State University, March 9-10, 2012.
  • Projective Representation of Non-Representable Matroids (of Biased Graphs). The Combinatorics Seminar, Binghamton University, Binghamton NY, May 23, 2011.
  • A representation of the bias matroid in a projective plane. Combinatorics seminar, Dept of Mathematics, University of South Carolina, Columbia, April 20 2011.
  • Some open questions. Regional Campuses Mathematics Seminar, University of South Carolina Sumter, Sep 17, 2010.
  • Harmonic Conjugation and Projective Rectangles. The Combinatorics Seminar, Binghamton University, Binghamton NY, May 25, 2010 .
  • A construction of a projective rectangle in a full algebraic matroid. Spring Southeastern Sectional Meeting, University of Kentucky, Lexington, KY, March 28, 2010.
  • Some topics in harmonic matroids. Regional Campuses Mathematics Seminar, University of South Carolina Lancaster, October 30, 2009.
  • A representation of the bias matroid in a projective plane. Fortieth Southeastern International Conference on Combinatorics, Graph Theory and Computing, March 2-6, 2009. Florida Atlantic University, Boca Raton.
  • Merging the Streams: Interdisciplinary Approaches to Improving Undergraduate Education and Civic Engagement. SENCER Summer Institute, San Jose CA, August 10, 2008.
  • A family of non-orientable matroids of rank three in a projective plane. American Mathematical Society (AMS) Joint Mathematics Meetings, San Diego CA, January 6, 2008.
  • What is a matroid?. The Mathematical Association of America (MAA) MAA/SIAM-SE conference at Georgia Southern University in Statesboro, Georgia. March 16, 2007.
  • A construction of a projective plane in a full algebraic matroids. Combinatorics seminar, Dept of Mathematics, University of South Carolina, February 28 2007.
  • Minimal non-orientable matroids in projective planes.  The 28th  Ohio State-Denison, Mathematics conference, Columbus Oh, May 21, 2006.
  • A Construction of a projective plane in harmonic matroids. American Mathematical Society (AMS) Joint Mathematics Meetings, San Antonio TX, January 13 2006.
  • Harmonic matroids as a tool to prove some conjectures in algebraic matroids. Combinatorics seminar, Dept of Mathematics, University of South Carolina, Columbia, September 22 2005.
  • Introduction to matroids II. Combinatorics seminar, Dept of Mathematics, University of South Carolina, Columbia, September 15 2005.
  • Introduction to matroids I. Combinatorics seminar, Dept of Mathematics, University of South Carolina, Columbia, September 8 2005
  • A conjecture of Lindstrom on a class of algebraically non-representable matroids. Discrete Geometry &Combinatorics Seminar, Dept of mathematics, Cornell University, March 9 2005.
  • Harmonic matroids and a conjecture of Lindstrom's. Mathematics Seminar, Scranton University, February 24 2005.
  • Harmonic Conjugation in Harmonic Matroids. Combinatorics and Number Theory Seminar, Dept. of Mathematical Sciences, Binghamton University, February 17 2005.
  • How the harmonic conjugate works in the algebraic matroids to construct algebraically nonrepresentable matroids. American Mathematical Society (AMS) Joint Mathematics Meetings, Atlanta GA, January 6 2005.
  • What is a matroid and what is it for? Mathematical Association of America (MAA) Seaway Section at Canisius College, Buffalo, NY, November 6 2004.
  • Lindstrom's Conjecture on a Class of Algebraically Non-Representable Matroids. Combinatorics and Number theory Seminar, Dept. of Mathematical Sciences,
  • Binghamton University, October 1 2004.
  • Pseudomodularity and Full Algebraic Matroids. Algebra Seminar, Dept. of Mathematical Sciences, Binghamton University, March 25 2003.
  • The Relationship Between Full Algebraic Matroids and Lattice Properties: Pseudomodularity and Double Circuits. Combinatorics and Number Theory Seminar, Dept. of Mathematical Sciences, Binghamton University, March 24 2003.
  • Tutte-Grothendieck Invariance and the Chromatic and Characteristic Polynomials. Combinatorics and Number Theory Seminar, Dept. of Mathematical Sciences, Binghamton University, March 6 2002.
The views and opinions expressed in this page are strictly those of Rigoberto Florez. The contents of this page have not been reviewed or approved by The Citadel.