2024.03 ~ current Professor, Department of Mathematics, Kyung Hee University, Seoul, Korea
2019.09 ~ 2024.02 Associate professor, Department of Mathematics, Kyung Hee University, Seoul, Korea
2019.03 ~ 2019.08 Associate professor (early promotion), Department of Mathematics, Duksung Women's University, Seoul, Korea
2014.03 ~ 2019.02 Assistant professor, Department of Mathematics, Duksung Women's University, Seoul, Korea
2013.03 ~ 2014.02 Postdoctoral fellow of ASARC, Korea Advanced Institute of Science and Technology, Daejeon, Korea
EDUCATION
2007.09 ~ 2012.05 Ph.D. in Mathematics at Emory University, USA (Advisor: Vojtech Rödl)
1997.03 ~ 2002.02 B.S. in Mathematics at Seoul Nat'l University, Korea
RESEARCH, TEACHING, or OTHER INTERESTS
Discrete Mathematics and Combinatorics, Mathematics
On Graham partitions twisted by the Legendre symbol Byungchan Kim, Ji Young Kim, Chong Gyu Lee, Sang June Lee, Poo-Sung Park, et al. Open Mathematics, 2023 We investigate when there is a partition of a positive integer n n , n = f ( λ 1 ) + f ( λ 2 ) + ⋯ + f ( λ ℓ ) , n=f\\left({\\lambda }_{1})+f\\left({\\lambda }_{2})+\\cdots +f\\left({\\lambda }_{\\ell }), satisfying that 1 = χ p ( λ 1 ) λ 1 + χ p ( λ 2 ) λ 2 + ⋯ + χ p ( λ ℓ ) λ ℓ , 1=\\frac{{\\chi }_{p}\\left({\\lambda }_{1})}{{\\lambda }_{1}}+\\frac{{\\chi }_{p}\\left({\\lambda }_{2})}{{\\lambda }_{2}}+\\cdots +\\frac{{\\chi }_{p}\\left({\\lambda }_{\\ell })}{{\\lambda }_{\\ell }}, where χ p {\\chi }_{p} is the Legendre symbol modulo prime p p and f ( k ) = k f\\left(k)=k or the k k th m m -gonal number with m = 3 m=3 , 4, or 5.
On strong Sidon sets of integers Yoshiharu Kohayakawa, Sang June Lee, Carlos Gustavo Moreira, Vojtěch Rödl Journal of Combinatorial Theory Series A, 2021
Detecting and Recovering Integer Data Manipulated by Multiplication with a Nonintegral Real Number and a Rounding Operation Taejung Park, Hyunjoo Song, Sang June Lee IEEE Access, 2021 This paper presents a method for detecting and restoring integer datasets that have been manipulated by operations involving nonintegral real-number multiplication and rounding. As we discuss in the paper, detecting and restoring such manipulated integer datasets is not straightforward, nor are there any known solutions. We introduce the manipulation process, which was motivated by an actual case of fraud, and survey several areas of literature dealing with the possibility that manipulation may have happened or might occur. From our mathematical analysis of the manipulation process, we can prove that the nonintegral real number (<inline-formula> <tex-math notation="LaTeX">$\\alpha $ </tex-math></inline-formula>) used in the multiplication exists not as a single real number but as an interval containing infinitely many real numbers, any of which could have been used to produce the same manipulation result. Based on these analytic findings, we provide an algorithm that can detect and restore manipulated integer datasets. To validate our algorithm, we applied it to 40,000 test datasets that were randomly generated using controllable parameters that matched the real fraud case. Our results indicated that the algorithm detected and perfectly restored all datasets for which the value of the nonintegral real number was at least 16 (<inline-formula> <tex-math notation="LaTeX">$\\alpha \\geq 16$ </tex-math></inline-formula>) and the number of data entries was at least 40 (<inline-formula> <tex-math notation="LaTeX">$n\\geq 40$ </tex-math></inline-formula>).
On the total variation distance between the binomial random graph and the random intersection graph Jeong Han Kim, Sang June Lee, Joohan Na Random Structures and Algorithms, 2018 When each vertex is assigned a set, the intersection graph generated by the sets is the graph in which two distinct vertices are joined by an edge if and only if their assigned sets have a nonempty intersection. An interval graph is an intersection graph generated by intervals in the real line. A chordal graph can be considered as an intersection graph generated by subtrees of a tree. In 1999, Karoński, Scheinerman, and Singer‐Cohen introduced a random intersection graph by taking randomly assigned sets. The random intersection graph has n vertices and sets assigned to the vertices are chosen to be i.i.d. random subsets of a fixed set M of size m where each element of M belongs to each random subset with probability p, independently of all other elements in M. In 2000, Fill, Scheinerman, and Singer‐Cohen showed that the total variation distance between the random graph and the Erdös‐Rényi graph tends to 0 for any if , where is chosen so that the expected numbers of edges in the two graphs are the same. In this paper, it is proved that the total variation distance still tends to 0 for any whenever .
The number of B h -sets of a given cardinality: Domingos Dellamonica, Yoshiharu Kohayakawa, Sang June Lee, Vojtěch Rödl, Wojciech Samotij Proceedings of the London Mathematical Society, 2018 For any integer h⩾2 , a set A of integers is called a Bh ‐set if all sums a1+⋯+ah , with a1,…,ah∈A and a1⩽⋯⩽ah , are distinct. We obtain essentially sharp asymptotic bounds for the number of Bh ‐sets of a given cardinality that are contained in the interval {1,⋯,n} . As a consequence of these bounds, we determine, for any integer m⩽n , the cardinality of the largest Bh ‐set contained in a typical m ‐element subset of {1,…,n} .
The number of B3-sets of a given cardinality Domingos Dellamonica, Yoshiharu Kohayakawa, Sang June Lee, Vojtěch Rödl, Wojciech Samotij Journal of Combinatorial Theory Series A, 2016
On the Number of Bh-Sets DOMINGOS DELLAMONICA, YOSHIHARU KOHAYAKAWA, SANG JUNE LEE, VOJTĚCH RÖDL, WOJCIECH SAMOTIJ Combinatorics Probability and Computing, 2016
