
MACS
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, and J. L. Ramirez, Enumerating Symmetric and Asymmetric Peaks in Dyck paths. Submitted.
 H. Ching, R. Florez and A. Mukherjee, Families of Integral Graphs with at most Five Distinct Eigenvalues. Submitted.
 R. Florez and A. Mukherjee, Proof without words Factorials as products of triangular numbers. Submitted.
 R. Florez, L. Junes, and J. L. Ramirez,
Counting pyramids in nondecreasing Dyck paths.
Submitted.
 R. Florez and D. Narayan,
Minimally NonAsymmetric Graphs and Balanced Incomplete Block Designs.
Submitted.
 R. Florez and J. L. Ramirez,
Enumerations of tDyck paths with nondecreasing valleys.
Submitted.
 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.
 A. Brewer, R. Florez, A. Gregory, Q. Jones, D. Narayan, and L. Rodriguez,
Infinite Families of Asymmetric Graphs.
Accepted for publication by AKCE International Journal of Graphs and Combinatorics.
 R. Florez, R. Higuita,
Another proof for partial strong divisibility property of Lucastype Polynomials.
The Fibonacci Quarterly 58.1 (2020), 7072. A version in
FQ
 R. Florez and T. Zaslavsky, Projective Planarity of Matroids of 3Nets and Biased Graphs.
76.2 (2020), 299–338.
A version in Australasian Journal of Combinatorics or in ArXiv.
 R. Florez and A. Mukherjee, Classroom experiences in introducing students to conjectures, exploration and visual proofs using experiments on the mobius strip. PRIMUS. 30.1 50–66, 2020. A version in PRIMUS
 M. Blair, R. Florez, and A. Mukherjee,
Matrices in the Hosoya Triangle.
The Fibonacci Quarterly, 57.5 (2019), 1528. A version in
FQ
or
ArXiv.
 R. Florez, L. Junes, and J. L. Ramirez,
Enumerating several aspects of nondecreasing Dyck paths.
Discrete Mathematics, 342.10 (2019), 30793097.
 R. Florez, R. Higuita, and A. Ramirez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials.
Journal of Integer Sequences, Vol. 22 (2019). Article 19.4.4.
A free version JIS or
ArXiv.
 R. Florez and T. Zaslavsky, Biased Graphs. VI. Synthetic Geometry. European J. Combin. 81 (2019), 119141. A version in ArXiv.
 R. Florez, E. Carter, B. Ek, D. A. Gonzalez, and D. Narayan, Intersecting Geodesics and Centrality Graphs. InvolveA journal of Mathematics, 12.1 (2019), 3143.
 E. Czabarka, R. Florez, L. Junes, and J. L. Ramirez,
Enumerations of Peaks and Valleys on Nondecreasing Dyck Paths.
Discrete Mathematics, 341.10 (2018), 27892807.
 R. Florez and J. L. Ramirez, Some Enumerations on NonDecreasing Motzkin Paths.
Australasian Journal of Combinatorics, 72.1 (2018), 138154.
A free version Australasian Journal of Combinatorics
 R. Florez, O. Haynes, D. Narayan and A. Strang, Enumerating shortest paths and determining edge betweenness centrality in Cartesian products of paths and cycles. Bulletin of ICA, Vol. 83 (2018), 2951.
 R. Florez, R. Higuita, and A. Mukherjee, Star of David and other patterns in the Hosoyalike 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. Florez, L. Junes, and J. L. Ramirez, Further Results on Paths in an nDimensional 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), 17. Nonfree 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 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), 583592. MR3630305
 B. Baker Swart, R. Florez, D. Narayan, and G. Rudolph, Extrema Property of the kRanking of Directed Paths and Cycles. AKCE International Journal of Graphs and Combinatorics, 2.6 (2016), 116. MR3524756. Free version AKCEVol131 or AKCEVol 131. A version in ArXiv.
 R. Florez and D. A. Narayan, Maximizing the number of edges in optimal krankings. AKCE International Journal of Graphs and Combinatorics, 12.1 (2015), 18. MR3410846. Free Version AKCEVol 101. 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), 122. MR3303767. Free Version JISVol 181
 E. Czabarka, R. Florez, and L. Junes, Some Enumerations on Nondecreasing Dyck Paths, The Electronics Journal of Combinatorics, 22.1 (2015) 122. MR3315445. Free version EJCVol 22
 R. Florez, R. Higuita and L. Junes, 9modularity and GCD Properties of Generalized Fibonacci Numbers, Integers, 14 (2014), 114. MR3268585. Free version INTVol 14
 R. Florez, R. Higuita and A. Mukherjees, Alternating sums in the Hosoya polynomial triangle, Journal of Integer Sequences, 17.9 (2014), 117. MR3261053. Free Version JISVol 179
 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. 117. Free Version JISVol 174
 R. Florez and L. Junes, GCD properties in the Hosoya's Triangle.The Fibonacci Quarterly 50.2 (2012). MR2927935. Free version The Fibonacci Quaterly.
 R. Florez and L. Junes, A Relation Between Triangular
Numbers and Prime Numbers. Integers, 12 (2012), no. 1, 8396. MR2955583. Free version INTVol 11, other version is at INTEGERS.
 R. Florez and D. A. Narayan, An optimal kranking
characterization of oriented paths and cycles, Bulletin of the
Institute of Combinatorics and Its Applications, 61 (2011) 97108. MR2724560
 R. Florez, Harmonic conjugation in harmonic matroids.
Discrete Mathematics, 309 (2009), 23652372. MR2276967
 R. Florez and D. Forge, Minimal nonorientable matroids in
a projective plane, Journal of Combinatorial Theory Series A, 114
(2007), 175183. MR2276967
 R. Florez, Lindstrom's conjecture on a class of algebraically
nonrepresentable matroids. European Journal of Combinatorics, 27
(2006), 896905. 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: 9780542192173. MR2707450
 R. Florez and J. Velez, Failure of splitting from modulefinite
extension rings. Beitrage zur Algebra und Geometrie
(contributions to algebra and geometry), 41 (2000), 345357. MR1801426. Free version Beitr. Algebra Geom. Vol 41


Papers Presented:
 More about projective rectangles. Fall Eastern Sectional Meeting, Binghamton, NY Oct 12, 2019. Special Session on Algebraic Combinatorics on the Occasion of the 75th Birthday of Thomas Zaslavsky, 2019.
 Projective Rectangles. Colloquia, Department of Mathematics, College of Charleston, Sept 20, 2019.
 The strong divisibility property and the resultant of generalized Fibonacci polynomials. XXII Congreso Colombiano de Matematicas, Popayan (Colombia), June 11, 2019. A semiplenary speaker.
 Projective Rectangles. New York Combinatorics Seminar, CUNY Graduate Center's Math Department and Computer Science Department, March 15, 2019.
 Projective Rectangles. Discrete/Combinatorics, University of South Carolina Feb 15, 2019.
 The strong divisibility property and the resultant of generalized Fibonacci polynomials. Discrete/Combinatorics & Number Theory Crossover Seminar, University of South Carolina Oct 12, 2018.
 The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials. INTEGERS Conference 2018, Augusta, Georgia October 6, 2018.
 Projective Planarity of 3Nets and Biased Graphs. 2018 SIAM Conference on Discrete Mathematics, Denver CO, June 6, 2018.
 The Geometry of some Fibonacci identities in the Hosoya triangle. MAA Southeastern Section Spring 2018 Meeting, Clemson University, March 2324, 2018.
 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 72016, 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.
 Nondecreasing 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 NonRepresentable Matroids (of Biased Graphs). Discrete Seminar, University of South Carolina Feb 12, 2016.
 Projective Representation of NonRepresentable 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 brownbag 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 NonDecreasing Dyck Paths. Discrete Seminar, University of South Carolina Nov 21, 2014.
 A formal Power Series to Count nondecreasing 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 1719, 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 910, 2012.
 Projective Representation of NonRepresentable 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 26, 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 nonorientable 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/SIAMSE 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 nonorientable matroids in projective planes. The 28th Ohio StateDenison, 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
nonrepresentable 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
NonRepresentable 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.
 TutteGrothendieck 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.


