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 J.R.Cho, my M.S. advisor) Bounds on the Size of Orbits of the Permutation Groups with bounded movement, M.S. thesis.

 (With J.D.H. Smith, my Ph.D. advisor) Orbit Decomposition in the Distinct and Bi-restricted Power of a Permutation Representation, ISU Math. Rep., 00-18, 2000

 (With J.D.H. Smith) The Tri-restricted Numbers and Powers of Permutation Representations, J. Comb. Math. Comb. Comp. 42 (2002), 113-125.

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

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

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

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

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

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

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

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

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

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

 

 

Undergraduate Research at Shippensburg

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

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

 

Math elsewhere

 American Mathematics Society (AMS)

 The Mathematical Association of America (MAA)

 Combinatorics and Algebra Seminar at ISU

 Linear Algebra: Matrix Completions Research Group

 Midwest Conference of Coding, Combinatorics, and Cryptography (MCCCC)

·  The Korean Mathematical Society (KMS)

·  Korean-American Scientists and Engineers Association(KSEA)