About Research

Interest

Anything with Algebra; Algebra, Combinatorics, Algebraic Combinatorics, Combinatorial Algebra, Graph Theory, Cryptography, Game Theory, Prime Numbers, Puzzles, Graph Pebbling, Universal Algebra, Music, Human and Alien being, etc.

Paper

· (With D.E. Ensley and J. Hoover ) Some Identities on Generalized Arithmetic Triangles , Mathematics Magazine (2024), 1-17

· Generating b-nomial numbers , Communications on Number Theory and Combinatorial Theory, Vol 3(2022), Article 1

· Digit sums generalizing binomial coefficients, J. Integer Seq., 22 (2019), Article 19.8.3

· Indispensable digits for digit sums , Notes Number Theory Discrete Math, 25 (2019), 40-48

· Digit sums and vertex-labelings , Advances and Applications in Discrete Mathematics, 9 (2018), 3, P.321..337

· A generalization of Collatz functions and Jacobsthal numbers , J. Integer Seq., 21 (2018), Article 18.5.4

· Ternary modified Collatz sequences and Jacobsthal numbers, J. Integer Seq., 19 (2016), Article 16.75

·Multi-restrained Stirling numbers, Ars. Com. CXX (2015), pp. 113-127

·(with J.D.H. Smith) Recurrences for Tri-restricted numbers, J. Comb. Math. Comb. Comp., 58 (2006), 3-11

·(with Long, Ng, Smith) Reciprocity for Stirling and multirestricted numbers, J. Comb. Th., Ser. A, 113 (2006), 1050-1060

·(With J.D.H. Smith) On the combinatorics of multi-restricted numbers, Ars. Com., 75 (2005), 44-63.

·(With DeAlba, Hogben, Kivunge, Nordstrom, Shedenhelm) The Nonnegative P0-Matrix Completion Problem, ELA, 10 (2003), 46-59.

·(With J.D.H. Smith) On the Unimodality and Combinatorics of the Bessel Numbers, Discrete Math., 264 (2003), 45-53.

·(With DeAlba, Hogben, Maxwell, Wangsness) The P_0-matrix completion problem, ELA, 9 (2002), 1-20.

· (With J. D. H. Smith) The tri-restricted numbers and powers of permutation representations, J. cob. Math. Cob. Comp., 42 (2002), 113 - 125.

· (With J. D. H. Smith) Orbit decomposition in the distinct and bi-restricted power of a permutation representation , ISU Math Rep., (2000), 00 - 18

· Bounds on the Size of Orbits of the Permutation Groups with bounded movement M.S. thesis. supervised by Dr. J. R. Cho (1996)

Undergraduate Research at Shippensburg

ï¿½ Justin Baker Graph Pebbling numbers of the cycles attached an edge, (2004-2005)

· Kelly Toppin Minimum Pk-total weights of complete graphs, (2008-2009)

· Ibrahim Abdurrahman Possible counterexamples on Collatz Conjucture, (2012-2013)

· Conner Oldt Optimization on cooking pizzas, (2018-2019)

· Jacob Smith An Exploration Of Divisibility(2019-2020)

· Jessica Champion Golden Ratio, Pi, and e (2020-Present)

Math elsewhere

ï¿½ American Mathematics Society (AMS)

ï¿½ The Mathematical Association of America (MAA)

ï¿½ Combinatorics and Algebra Seminar at ISU

Undergraduate Research at Shippensburg

ï¿½ Justin Baker Graph Pebbling numbers of the cycles attached an edge, (2004-2005)

· Kelly Toppin Minimum Pk-total weights of complete graphs, (2008-2009)

· Ibrahim Abdurrahman Possible counterexamples on Collatz Conjucture, (2012-2013)

· Conner Oldt Optimization on cooking pizzas, (2018-2019)

· Jacob Smith An Exploration Of Divisibility(2019-2020)

· Jessica Champion Golden Ratio, Pi, and e (2020-Present)

Math elsewhere

ï¿½ Linear Algebra: Matrix Completions Research Group

ï¿½ Midwest Conference of Coding, Combinatorics, and Cryptography (MCCCC)

· The Korean Mathematical Society (KMS)

· Korean-American Scientists and Engineers Association(KSEA)