Publications
My published work includes research in number theory, combinatorics, algebra, discrete mathematics, and related areas, together with an extensive body of collaborative work with undergraduate students.
Research Publications
- 2025 Counting Subwords in Non-Decreasing Dyck Paths Journal of Integer Sequences, Vol. 28 (2025), Article 25.1.6 · Abstract
- 2021 Counting Asymmetric Weighted Pyramids in Non-Decreasing Dyck Paths Australasian Journal of Combinatorics, 79.1 (2021), 123–140 · PDF
- 2019 Enumerating Several Aspects of Non-Decreasing Dyck Paths Discrete Mathematics, 342.10 (2019), 3079–3097 · DOI
- 2018 Enumerations of Peaks and Valleys on Non-Decreasing Dyck Paths Discrete Mathematics, 341.10 (2018), 2789–2807 · DOI
- 2018 Further Results on Paths in an n-Dimensional Cubic Lattice Journal of Integer Sequences, Vol. 21 (2018), Article 18.1.2 · Abstract
- 2015 A Discrete Convolution on the Generalized Hosoya Triangle Journal of Integer Sequences, Vol. 18 (2015), Article 15.1.6 · Abstract
- 2015 Some Enumerations on Non-Decreasing Dyck Paths Electronic Journal of Combinatorics, Vol. 22, Issue 1 (2015) · DOI
- 2014 GCD Property of the Generalized Star of David in the Generalized Hosoya Triangle Journal of Integer Sequences, Vol. 17 (2014), Article 14.3.6 · Abstract
- 2014 9-Modularity and GCD Properties of Generalized Fibonacci Numbers Electronic Journal of Combinatorial Number Theory, Vol. 14 (2014), Article A55 · PDF
- 2012 Teaching Inverse Functions with Cryptography Memoirs of the 12th International Congress on Mathematical Education, Seoul, South Korea, July 8–15, 2012
- 2012 GCD Properties in Hosoya's Triangle The Fibonacci Quarterly, 50.2 (2012), 163–174 · PDF
- 2011 A Relation Between Triangular Numbers and Prime Numbers Electronic Journal of Combinatorial Number Theory, Vol. 11 (2011), Article A50 · PDF
- 2010 A Duality Theorem in Oriented Matroids Memoirs of the Fourth International Conference of Algebra, Number Theory, Combinatorics and Applications, Tunja, Colombia, May 2010
Publications with Students
These publications arose from undergraduate research collaborations involving students in the United States and Colombia.
- 2023 A Depressed Quartic Equation with Fibonacci Coefficients The Fibonacci Quarterly, 61.4, 370 · PDF
- 2023 This Time, It Is d'Ocagne's Turn The Fibonacci Quarterly, 61.3, 281 · PDF
- 2023 It's Catalan Again! The Fibonacci Quarterly, 61.3, 280 · PDF
- 2023 It's All About Catalan The Fibonacci Quarterly, 61.3, 277 · PDF
- 2021 An Unusual Sum of Products The Fibonacci Quarterly, 59.3, 279 · PDF
- 2021 Apply the Triangle Inequality The Fibonacci Quarterly, 59.3, 278 · PDF
- 2021 A Summation Formula for an Arithmetic Progression The Fibonacci Quarterly, 59.3, 277 · PDF
- 2021 A Binomial Sum of Cosine and Sine Functions The Fibonacci Quarterly, 59.3, 276 · PDF
- 2021 Three Atypical Solutions The Fibonacci Quarterly, 59.3, 275 · PDF
- 2021 The Fifth Oldie from the Vault The Fibonacci Quarterly, 59.3, 274 · PDF
- 2021 An Inequality in Two Variables The Fibonacci Quarterly, 59.2, 183 · PDF
- 2021 Prove It in Any Way You Like The Fibonacci Quarterly, 59.2, 180 · PDF
- 2021 The Zeta Riemann Function and the Cotangent Function The Fibonacci Quarterly, 59.2, 179 · PDF
- 2021 A Nested Radical of Ones The Fibonacci Quarterly, 59.2, 178 · PDF
- 2019 Generating Function of the Catalan Numbers The Fibonacci Quarterly, 57.2, 178 · PDF
- 2019 The Generating Function for Harmonic Numbers The Fibonacci Quarterly, 57.1, 83 · PDF
- 2019 Determinant of a Symmetric Matrix The Fibonacci Quarterly, 57.1, 82 · PDF
- 2018 Bergstrom on a Cyclic Sum The Fibonacci Quarterly, 56.2, 180 · PDF
- 2016 Closure! The Fibonacci Quarterly, 54.4, 368 · PDF
- 2015 It Can Be Sharpened The Fibonacci Quarterly, 53.2, 181 · PDF
- 2015 Close This Sum The Fibonacci Quarterly, 53.2, 182 · PDF
- 2014 The AM-GM Inequality Paves the Way The Fibonacci Quarterly, 52.3, 276 · PDF
- 2014 The Value of a Series of Reciprocal Fibonacci Numbers The Fibonacci Quarterly, 52.3, 277 · PDF
- 2014 Nth Root of a Product The Fibonacci Quarterly, 52.2, 179 · PDF
- 2014 It Could Be A Rational Bound The Fibonacci Quarterly, 52.2, 181 · PDF
- 2014 Inequalities Generalized The Fibonacci Quarterly, 52.2, 182 · PDF
- 2014 Almost Déjà vu! The Fibonacci Quarterly, 52.2, 183 · PDF
- 2013 Another Division by 5 The Fibonacci Quarterly, 51.4, 369 · PDF
- 2013 Two Sums with Square Roots The Fibonacci Quarterly, 51.4, 370 · PDF
- 2013 A Trig and Fibonacci Amalgam The Fibonacci Quarterly, 51.4, 373 · PDF
- 2013 Periodic Sequences The Fibonacci Quarterly, 51.4, 373 · PDF
- 2013 Fibonacci Numbers Divided by 11 The Fibonacci Quarterly, 51.3, 276 · PDF
- 2013 The Fifth and Seven Powers of Fibonacci Numbers The Fibonacci Quarterly, 51.3, 278 · PDF
- 2013 Evaluating a Double Sum with Inverse Fibonacci Numbers The Fibonacci Quarterly, 51.2, 180 · PDF
- 2013 A Fibonacci and Triangular Numbers Inequality The Fibonacci Quarterly, 51.2, 182 · PDF
- 2013 The Ubiquitous AM-GM Inequality The Fibonacci Quarterly, 51.1, 86 · PDF
- 2013 From the Weighted AM-GM Inequality The Fibonacci Quarterly, 51.1, 87 · PDF
- 2013 An Extension to Negative Subscripts The Fibonacci Quarterly, 51.1, 88 · PDF
- 2012 By Means of the Geometric and Arithmetic Means The Fibonacci Quarterly, 50.4, 369 · PDF
- 2012 A Rate of Growth of Sum of Reciprocal Fibonacci Numbers The Fibonacci Quarterly, 50.3, 274 · PDF
- 2012 It Is Two! The Fibonacci Quarterly, 50.2, 182 · PDF
- 2012 It Is Two, Too! The Fibonacci Quarterly, 50.2, 183 · PDF
- 2012 A "Well-Connected" Sequence The Fibonacci Quarterly, 50.2, 184 · PDF
- 2012 A "Loaded Divisibility" Problem The Fibonacci Quarterly, 50.2, 185 · PDF
- 2012 A "Sterling" Sum The Fibonacci Quarterly, 50.2, 186 · PDF
Books in Preparation
Not yet published, and not counted above.
- Some Topics in Number Theory In preparation
- An Introduction to Cryptography with Python: A Beginner's Guide In preparation