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SOME HOMOGENEITY CLASSES OF POSETS OF HEIGHT 2
채갑병,정민석,김상목 대한수학회 2012 대한수학회보 Vol.49 No.2
In this paper, we find the inclusion relation among four categories of posets,i.e., ideal-homogeneous, tower-homogeneous, quasi-com\-plement-preserved, and complement-preserved posets.
INCLUSION AND EXCLUSION FOR FINITELY MANY TYPES OF PROPERTIES
채갑병,정민석,김상목 호남수학회 2010 호남수학학술지 Vol.32 No.1
Inclusion and exclusion is used in many papers to count certain objects exactly or asymptotically. Also it is used to derive the Bonferroni inequalities in probabilistic area [6]. Inclusion and exclusion on ¯nitely many types of properties is first used in R. Meyer [7] in probability form and first used in the paper of McKay,Palmer, Read and Robinson [8] as a form of counting version of inclusion and exclusion on two types of properties. In this paper,we provide a proof for inclusion and exclusion on finitely many types of properties in counting version. As an example, the asymptotic number of general cubic graphs via inclusion and exclusion formula is given for this generalization.
Enumeration of optimally labelled graphs of bandwidth 2
채갑병,정민석,김상목 대한수학회 2017 대한수학회보 Vol.54 No.6
An optimally labelled graph of bandwidth 2 is an ordered pair $(G, f)$ where $G$ is a simple graph with $bw(G)=2$ and $f : V(G) \rightarrow [n]$ is a bijection such that $bw(G, f)=2$. In this paper, the number of optimally labelled graphs of bandwidth two of order $n$ is enumerated by counting linear forests.
Asymptotic number of General Cubic Graphs with given Connectivity
채갑병 대한수학회 2005 대한수학회지 Vol.42 No.6
Let g(2n,l,d) be the number of general cubic graphs on 2n labeled vertices withl loops and d double edges. We use inclusion and exclusion with two types ofproperties to determine the asymptotic behavior of g(2n,l,d) and hence that ofg(2n), the total number of general cubic graphs of order 2n. We show that almostall general cubic graphs are connected. Moreover, we determined the asymptoticnumbers of general cubic graphs with given connectivity.
ENUMERATION OF OPTIMALLY LABELLED n-POSETS OF LINEAR DISCREPANCY TWO
채갑병 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.4
Any labelled n-poset of linear discrepancy two can be writ- ten in terms of matrix representations. But there are matrices which are not the adjacency matrices of the comparability graphs of any poset at all, say non-poset matrices of order n, and matrices which are of tight- ness two but of linear discrepancy one, say non-optimal labelled matrices of order n in matrix representations. In this paper, the number of opti- mally labelled n-posets of linear discrepancy two is obtained by count- ing the number of non-poset matrices and the number of non-optimal labelled matrices.
Interval-valued intuitionistic sets and their application to topology
채갑병,김준희,이정곤,허걸 원광대학교 기초자연과학연구소 2021 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.21 No.1
In this paper, we introduce the new notion of interval-valued intuitionistic sets providing a tool for approximating undefinable or complex concepts. First, we deal with some of its algebraic structures. Also, we define an interval-valued intuitionistic (vanishing) point and obtain some of its properties. Next, we define an interval-valued intuitionistic topology, base (subbase), neighborhood and interior (closure), respectively and study some of each properties, and give some examples.
THE NUMBER OF NON-POSET MATRICES
채갑병,정민석,김상목 장전수학회 2016 Proceedings of the Jangjeon mathematical society Vol.19 No.4
Any labelled n-poset can be written in terms of matrix representation. This matrix is called the labelled matrix of a labelled n- poset. In point of view of graph theory, the labelled matrix of a labelled n-poset is the adjacency matrix of the comparability graph of a labelled n-poset. There are matrices which are not adjacency matrices of the comparability graphs of a labelled n-poset, say non-poset matrices of order n. In this paper, the number of non-poset matrices which are not adjacency matrices of the comparability graphs of the labelled n-posets of linear discrepancy two is obtained by using a method of the partitions of a number.
The number of $(d,k)$-hypertrees
채갑병,Wai-Cheong Siu 호남수학회 2017 호남수학학술지 Vol.39 No.4
In this paper, we define and enumerate two tree-like hypergraph structures which we call them $(d,k)$-trees and $d$-trees, where $d \geq 2$ and $k > 0$ are integers. These new definitions generalize traditional and HP-hypertrees.
Some families of ideal-homogeneous posets
채갑병,정민석,김상목 대한수학회 2016 대한수학회보 Vol.53 No.4
A partially ordered set $P$ is \textit{ideal-homogeneous} provided that for any ideals $I$ and $J$, if $ I\cong_{\sigma}J$, then there exists an automorphism $\sigma^*$ such that $\sigma^*|_I = \sigma$. Behrendt~\cite{Beh} characterizes the ideal-homogeneous partially ordered sets of height $1$. In this paper, we characterize the ideal-homogeneous partially ordered sets of height 2 and find some families of ideal-homogeneous partially ordered sets.
A characterization of $n$-posets of ld $n-k$ with simple posets
채갑병,정민석,김상목 대한수학회 2018 대한수학회보 Vol.55 No.3
A simple poset is a poset whose linear discrepancy increases if any relation of the poset is removed. In this paper, we investigate more important properties of simple posets such as its width and height which help to construct concrete simple poset of linear discrepancy $l$. The simplicity of a poset is similar to the ld-irreducibility of a poset. Hence, we investigate which posets are both simple and ld-irreducible. Using these properties, we characterize $n$-posets of linear discrepancy $n-k$ for $k=2,3$, and, lastly, we also characterize a poset of linear discrepancy $3$ with simple posets and ld-irreducible posets.