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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, The Geometry of some Fibonacci Identities in the Hosoya Triangle. Submitted. A version in ArXiv.
  • 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 polynomial triangles. Submitted. A version in ArXiv.
  • R. Florez and T. Zaslavsky, Biased Graphs. VI. Synthetic Geometry. Submitted. A version in ArXiv.
  • R. Florez and J. L. Ramirez, Some Enumerations on Non-Decreasing Motzkin Paths. Accepted for publication in The Australasian Journal of Combinatorics 2018.
  • R. Florez, O. Haynes, D. Narayan and A. Strang, Enumerating shortest paths and determining edge betweenness centrality in Cartesian products of paths and cycles. Accepted for publication in the Bulletin of the Institute of Combinatorics and Its Applications.
  • E. Czabarka, R. Florez, L. Junes, and J. L. Ramirez, Enumerations of Peaks and Valleys on Non-decreasing Dyck Paths. Accepted for publication in Discrete Mathematics.
  • R. Florez and A. Mukherjees, Introducing Students to Conjectures, Exploration and Visual Proofs using Experiments in Topology. Accepted for publication in PRIMUS.
  • R. Florez, E. Carter, B. Ek, D. A. Gonzalez, and D. Narayan, Intersecting Geodesics and Centrality Graphs. Involve-A journal of Mathematics. 12.1 (2019), 31-43.
  • R. Florez, R. Higuita, and A. Mukherjee, Star of David and other patterns in the Hosoya-like polynomials triangles. Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6. A free version JIS or ArXiv.
  • R. Florez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial. Integers, 18B (2018), Paper No. A2. A version in INTEGERS. A version in ArXiv.
  • R. Florez, R. Higuita and A. Mukherjees, Characterization of the strong divisibility property for generalized Fibonacci polynomials. Integers, 18 (2018), Paper No. A14. A version in INTEGERS. A version in ArXiv.
  • R. Forez, L. Junes, and J. L. Ramirez, Further Results on Paths in an n-Dimensional Cubic Lattice. Journal of Integer Sequences, Vol. 21 (2018), Article 18.1.2. A free version JIS
  • R. Florez, J. Lind, and D. Narayan, Betweenness centrality in organizational Structures. Congr. Numer. 228 (2017), 281–288.
  • 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. Free version AKCE. A version in ArXiv.
  • 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.