• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.375-382
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• 2017

We exhibit a one-to-one correspondence between 3-colored graphs and subarrangements of certain hyperplane arrangements denoted ${\mathcal{J}}_n$, $n{\in}{\mathbb{N}}$. We define the notion of centrality of 3-colored graphs, which corresponds to the centrality of hyperplane arrangements. Via the correspondence, the characteristic polynomial ${\chi}{\mathcal{J}}_n$ of ${\mathcal{J}}_n$ can be expressed in terms of the number of central 3-colored graphs, and we compute ${\chi}{\mathcal{J}}_n$ for n = 2, 3.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1595-1604
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• 2017

We give a complete formula for the characteristic polynomial of hyperplane arrangements ${\mathcal{J}}_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $1{\leq}i$, j, k, $l{\leq}n$. The formula is obtained by associating hyperplane arrangements with graphs, and then enumerating central graphs via generating functions for the number of bipartite graphs of given order, size and number of connected components.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.759-765
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• 2018

We use the finite method developed by C. Athanasiadis based on Crapo-Rota's theorem to give a complete formula for the characteristic polynomial of hyperplane arrangements ${\mathcal{J}}_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $1{\leq}i,j,k,l{\leq}n$.

• Journal of applied mathematics & informatics
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• v.4 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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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.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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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.