• 호남수학학술지
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• 제23권1호
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• pp.71-90
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• 2001

In this paper, we introduce the MarKov chain and hyperplane arrangement. we prove some properties determined by a hyperplane arrangement and give an example as an application of them.

• 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.

• 대한수학회논문집
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• 제17권3호
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• pp.439-449
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• 2002

If an arrangement admits a nice partition, or an arrangement is free, then the characteristic polynomial of the arrangement can be factored. It is known that a free arrangement does not always admit a nice partition. We show that even an inductively free arrangement does not always admit a nice partition.

• 대한수학회보
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• 제53권5호
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• pp.1281-1289
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• 2016

Richard Stanley suggested the problem of finding combinatorial proofs of formulas for counting regions of certain hyperplane arrangements defined by hyperplanes of the form $x_i=0$, $x_i=x_j$, and $x_i=2x_j$ that were found using the finite field method. We give such proofs, using embroidered permutations and linear extensions of posets.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.279-284
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• 1997

The purpose of this paper is to show that if A is a tame arrangement and a hyperplane H is ageneric then $A^{H}$ is also tame. Since free arrangements are tame we can say tame we can say that almost free arrangements are tame.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.634-639
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• 1998

A methodology based on the concept of variable string length GA(VGA) is developed for determining automatically the number of hyperplanes and their appropriate arrangement for modeling the class boundaries of a given training data set in RN. The genetic operators and fitness functionare newly defined to take care of the variability in chromosome length. Experimental results on different artificial and real life data sets are provided.

• 호남수학학술지
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• 제43권4호
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• pp.679-689
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• 2021

The first author suggested an exact volume formula of the hypercubes [0, 1]ⁿ clipped by several hyperplanes expressed directly in terms of linear coefficients of the hyperplanes. However, it requires awkward assumptions to apply the formula to various situations. We suggest a concrete method to overcome those restrictions for two or three hyperplanes using 𝜖-perturbation, which gives an exact value applicable for any kind of arrangement of hyperplanes with no consideration.