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123 results on '"Suh-Ryung Kim"'

1. Exploration of the Truth Values of Conditionals Set up in Everyday Context and in Open Sentences

Author

Kyung-Jin Lee, JinHyeong Park, and Suh-Ryung Kim

Abstract

This study aimed to design a task in an everyday context to support high school students' exploration of the truth values of propositional conditionals and to understand their difficulties. The results showed that students could identify that the truth value of a propositional conditional is determined by two variables (the truth values of the antecedent and the consequent) while organizing the propositional conditionals generated from the open sentence and that a social contract situation can help students understand why the truth value of a conditional with a false antecedent is true. The study also revealed that students' difficulties in determining the truth values of conditionals are closely related to the time variable in an everyday context and the confusion between conditionals and causality. The findings from this study on the strategy and difficulties exhibited by students when determining the truth value of everyday conditional sentences can inform future efforts to teach formal mathematics in real-world contexts.

Published
2024
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10. Matrix periods and competition periods of Boolean Toeplitz matrices

Author

Gi-Sang Cheon, Bumtle Kang, Suh-Ryung Kim, and Homoon Ryu

Subjects
Numerical Analysis, Algebra and Number Theory, 05C20, 05C50, 15B05, FOS: Mathematics, Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, Combinatorics (math.CO), Geometry and Topology
Abstract

In this paper, we study the matrix period and the competition period of Toeplitz matrices over a binary Boolean ring $\mathbb{B} = \{0,1\}$. Given subsets $S$ and $T$ of $\{1,\ldots,n-1\}$, an $n\times n$ Toeplitz matrix $A=T_n\langle S ; T \rangle$ is defined to have $1$ as the $(i,j)$-entry if and only if $j-i \in S$ or $i-j \in T$. We show that if $\max S+\min T \le n$ and $\min S+\max T \le n$, then $A$ has the matrix period $d/d'$ and the competition period $1$ where $d = \gcd (s+t \mid s \in S, t \in T)$ and $d' = \gcd(d, \min S)$. Moreover, it is shown that the limit of the matrix sequence $\{A^m(A^T)^m\}_{m=1}^\infty$ is a directed sum of matrices of all ones except zero diagonal. In many literatures we see that graph theoretic method can be used to prove strong structural properties about matrices. Likewise, we develop our work from a graph theoretic point of view.

Published
2023

44. Exponents of primitive directed Toeplitz graphs

Author

Gi-Sang Cheon, Suh-Ryung Kim, Ji-Hwan Jung, and Bumtle Kang

Subjects
Combinatorics, Vertex (graph theory), Algebra and Number Theory, Computer Science::Discrete Mathematics, Exponent, Digraph, Disjoint sets, Connectivity, Graph, Toeplitz matrix, Mathematics
Abstract

Given disjoint non-empty subsets S and T of {1,…,n−1}, a digraph D with the vertex set {1,2,…,n} is called a directed Toeplitz graph provided the arc i→j occurs if and only if i−j∈S or j−i∈T. We in...

Published
2020

45. On the minimum clique partitioning problem on weighted chordal graphs

Author

Suh-Ryung Kim, Yoshio Sano, Changseong Jo, and Jihoon Choi

Subjects
Combinatorics, General Computer Science, Computer Science::Discrete Mathematics, Chordal graph, Interval (graph theory), Clique (graph theory), MathematicsofComputing_DISCRETEMATHEMATICS, Theoretical Computer Science, Mathematics, Superclass
Abstract

In this paper, we introduce a new family of graphs which is a subclass of chordal graphs as well as a superclass of interval graphs and study it. Myung [8] proposed an algorithm for the minimum clique partitioning problem with constrained bounds in weighted interval graphs. We extend the family of interval graphs to the family of so called “interval-like graphs” to which Myung's algorithm is applicable and show that bull-free chordal graphs and diamond-free chordal graphs are interval-like graphs.

Published
2019

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