Mathematics Faculty & Staff

2005  PhD, Mathematics, University of Kentucky

2002  MA, Mathematics, University of Kentucky

1999  BA, Mathematics, Georgetown College

Dr. Dunkum's current research area is algebraic combinatorics and combinatorial representation theory.

• “Move-minimizing Puzzles and Diamond-colored Modular/Distributive Lattices”, with R. Donnelly, E. Donovan, and T. Schroeder, accepted pending revisions.
• “Olry Terquem’s Forgotten Problem and an Enumerative-Combinatorial Perspective on the Euclidean Algorithm,” with R. Donnelly and R. McCoy (WKU undergraduate student). 2024. Handbook of the History and Philosophy of Mathematical Practice, B. Sriraman (Editor). Springer Nature Switzerland AG (2024), 1189-1217. https://doi.org/10.1007/978-3-031-40846-5 146
• “Symmetric Fibonaccian distributive lattices and representations of the special linear Lie algebras”, with R. Donnelly, S. Malone (WKU graduate student), and A. Nance (MSU undergraduate student), Involve, a Journal of Mathematics 16-2 (2023), 201–226. DOI 10.2140/involve.2023.16.201
• “Explicit constructions of some infinite families of finite-dimensional irreducible representations of the type E6 and E7 simple Lie algebras,” with R. Donnelly and A. White (WKU Gatton student), Applicable Algebra in Engineering, Communication and Computing (2023), https://doi.org/10.1007/s00200-023-00603-9
• “Gelfand–Tsetlin-type weight bases for all special linear Lie algebra representations corresponding to skew Schur functions”, with R. Donnelly, Advances in Applied Mathematics 139 (August 2022).
• “Sign-alternating Gibonacci polynomials”, with R. Donnelly, M. Huber (WKU undergraduate student), and L. Knupp (WKU Gatton student), Enumerative Combinatorics and Applications 1:2 (2021). M. Dunkum p. 4
• “Counting odd numbers in truncations of Pascals Triangle,” with R. Donnelly, C. George (WKU undergraduate), and S. Schnake (MSU undergraduate), The Pentagon, 79(1), 12-28, 2019.
• “The Group Action Tri-cycle Theorem, with R. Donnelly, The American Mathematical Monthly, 126(2) (2019), 179-179.
• “Edge Integrity of Nearest Neighbor Graphs and Separator Theorems, with D. Lanphier, Discrete Mathematics 342 no. 9 (2019), 2664-2679.
• “Cuspidality of pullbacks of Siegel-Hilbert Eisenstein series on Hermitian symmetric domains, with D. Lanphier, Rocky Mountain Journal of Mathematics 44 (2) 2014, 497-519.
• “Vulnerability of Nearest Neighbor Graphs”, with D. Lanphier, Discrete Applied Mathematics, Volume 171 (2014), 42-52.
• “Destroying Cycles in Digraphs”, with P. Hamburger and A. Por, Combinatorica 31 (1)(2011) 55-66.

• HON 303: Independent Research (Lie Algebras) with S. McKean, Fall 2014
• MATH 100: Intermediate Algebra
• MATH 109: General Mathematics
• MATH 116: College Algebra (including a special section for the College of Health and Human Services)  
• MATH 117: Trigonometry
• MATH 122: Calculus of a Single Variable I
• MATH 132: Calculus of a Single Variable II
• MATH 136: Calculus I (including a special section for Honors)
• MATH 137: Calculus II (including special sections for Honors and the Gatton Academy)
• MATH 203: Statistics
• MATH 211: Math for Elementary Teachers I
• MATH 212: Math for Elementary Teachers II
• MATH 240: Geometry in Art and Architecture (equivalent to HUM 240)
• MATH 275: Special Topics (Independent Research: Fibonacci and Enumeration I and II with L. Knupp, Spring 2019 and Fall 2019) (Independent Research: Type E Discrete Lie Algebras with A. White, Spring 2020)
• MATH 307: Introduction to Linear Algebra
• MATH 310: Introduction to Discrete Mathematics (including one section with an Honors Enriched and Embedded course)
• MATH 317: Introduction to Algebraic Systems
• MATH 417: Algebraic Systems (including sections with a graduate component)
• MATH 475: Special Topics (Independent Research: Fibonacci and Enumeration III with L. Knupp, Spring 2020)
• MATH 517: Topics from Algebra
• MATH 590: Independent Study (Coxeter Group Actions) with S. Malone, D. Price, Ian Ray, Fall 2020.