• 대한수학회지
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• 제33권3호
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• pp.679-684
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• 1996

In this paper we try to investigate the connection between matroids and jump numbers. A couole of papers [3, 5] are known, but they discuss optimization problems with matroid structure. Here we calculate the jump numbers of some bipartite posets which are induced by matroids.

• 대한수학회보
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• 제43권1호
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• pp.17-25
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• 2006

We generalize the results about eigenvalues of random walks on central hyperplane arrangements computed by Bidigare, Hanlon and Rockmore to the cases of random walks on oriented matroids.

• 한국수학교육학회지시리즈A:수학교육
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• 제21권2호
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• pp.1-3
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• 1983

• 한국수학교육학회지시리즈A:수학교육
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• 제16권2호
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• pp.29-31
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• 1978

bipartite graph와 Euler graph의 정의를 사용하는 대신 이들 graph가 나타내는 특성을 사용하여 bipartite matroid와 Euler matroid를 정의하고 이들 matroid가 binary일 때 서로 dual 의 관계가 있음을 증명한다. 이 관계를 이용하여 bipartite graph와 Euler graph의 성질을 밝힐수 있다.

• 호남수학학술지
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• 제38권2호
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• pp.393-401
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• 2016

In this article, we study the matroid base polytope for a matroid obtained from another matroid by a series or parallel extension of an element. We express this polytope as a wedge of a polytope. In particular, we provide the facial structure of the matroid base polytope corresponding to a series-parallel matroid.

• 한국수학교육학회지시리즈A:수학교육
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• 제13권3호
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• pp.22-32
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• 1975

Matroid와 transversal theory에 관한 연구가 활발하게 진행되고 있다. 이 논문은 circuit matroid가 transversal이 되기 위한 필요 충분 조건을 지적하고 이를 증명한 것이다. 곧 어떤 graph의 circuit matroid가 transversal이 되기 위한 필요 충분 조건은 그 graph가 graph $K_4$거나 $C_{k}$ $^{2}$에 homeomorphic인 subgraph를 포함하지 않은 것이다. 증명의 방법으로는 주로 matroid의 cocircuit의 성질을 사용하여 transversal Matroid의 presentation을 적절하게 적용하고 graph의 reduction과 contraction을 이용한다.

• 대한수학회보
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• 제52권3호
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• pp.955-962
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• 2015

It has been established that the role played by complete graphs in graph theory is similar to the role Dowling group geometries and Projective geometries play in matroid theory. In this paper, we introduce a notion of H-tree, a class of representable matroids which play a similar role to trees in graph theory. Then we give some properties of H-trees such that when q = 0, then the results reduce to the known properties of trees in graph theory. Finally we give explicit expressions of the characteristic polynomials of H-trees, H-cycles, H-fans and H-wheels.

• 호남수학학술지
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• 제40권1호
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• pp.27-46
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• 2018

In this paper, (E, L)-preproximity and uniformity spaces in matriod theory as a generalized to a classical proximity and Uniformity spaces introduced by Csaszar [1] is introduced. Recently, Shi [17]-[18] introduced a new approach to the fuzzification of matroids.Here introduce (E, L)-preproximity and uniformity spaces, Uniformity and strong uniformity on (E, L)-fuzzifying matroid space, Not only study the properties of this new notions, but it has been generated (E, L)-fuzzifying matroid Space from (E, L)-preproximity and uniformity spaces. Next to introduced (E, L)-preproximity continuous in (E, L)-fuzzifying matroid space and used it in more properties. Finally we solve combinatorial optimizations problem via (E, L)-fuzzifying matroid space.

• 한국수학교육학회지시리즈A:수학교육
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• 제12권2호
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• pp.1-4
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• 1974

Matroid theory, which was first introduced in 1935 by Whitney (2), is a branch of combinational mathematics which has some very much to the fore in the last few years. H. Whitney had just spent several years working in the field of graph theory, and had noticed several similarities between the ideas of independence and rank in graph theory and those of linear independence and dimension in the study of vector spaces. A matroid is essentially a set with some kind of 'independence structure' defined on it. There are several known results concerning how matroids can be induced from given matroid by a digraph. The purpose of this note is to show that, given a matroid M$_{0}$ (N) and a digraph $\Gamma$(N), then a new matroid M(N) is induced, where A⊆N is independent in M(N) if and only if A is the set of initial vertices of a family of pairwise-vertex-disjoint paths with terminal vertices independent in M$_{0}$ (N).(N).

• Kyungpook Mathematical Journal
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• 제57권3호
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• pp.371-383
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• 2017

Let M be a matroid. We study the expansions of M mainly to see how the combinatorial properties of M and its expansions are related to each other. It is shown that M is a graphic, binary or a transversal matroid if and only if an arbitrary expansion of M has the same property. Then we introduce a new functor, called contraction, which acts in contrast to expansion functor. As a main result of paper, we prove that a matroid M satisfies White's conjecture if and only if an arbitrary expansion of M does. It follows that it suffices to focus on the contraction of a given matroid for checking whether the matroid satisfies White's conjecture. Finally, some classes of matroids satisfying White's conjecture are presented.