• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.445-453
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• 2007

Using Schensted Insertion and Deletion algorithm for shifted rim hook tableaux described in [7], we construct Schensted algorithm for shifted rim hook tableaux. This give us the combinatorial proof for the orthogonality of the second kind for the spin characters of $\tilde{S}n$.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.391-399
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• 2005

In this paper we present an algorithm based on network flow techniques which provides a solution for a combinatorial problem. Then, in order to provide all the solutions of this problem, we make use of an algorithm that given the bipartite graph $G=(V_1 {\cup}{V_2},\;E,\;{\omega})$ outputs the enumeration of all bipartite matchings of given cardinality v and cost c.

• Journal of Korean Institute of Industrial Engineers
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• v.35 no.1
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• pp.87-91
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• 2009

In the server disconnection problem, a network with m servers and their users is given and an attacker is to destroy a set of edges to maximize his net gain defined as the total disconnected utilities of the users minus the total edge-destruction cost. The problem is known to be NP-hard. In this paper, we study the server disconnection problem restricted to a ring network. We present an efficient combinatorial algorithm that generates an optimal solution in polynomial time.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.289-298
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• 2010

E$\breve{g}$ecio$\breve{g}$lu and Remmel [1] gave a combinatorial interpretation for the entries of the inverse Kostka matrix $K^{-1}$. Using this interpretation Sagan and Lee [8] constructed a sign reversing involution on special rim hook tableaux. In this paper we generalize Sagan and Lee's algorithm on special rim hook tableaux to give a combinatorial partial proof of $K^{-1}K=I$.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.349-356
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• 2008

In this paper, we generalize the Catalan number to the (n, k)-th Catalan numbers and find a combinatorial description that the (n, k)-th Catalan numbers is equal to the number of partitions of n(k-1)+2 polygon by (k+1)-gon where all vertices of all (k+1)-gons lie on the vertices of n(k-1)+2 polygon.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.425-437
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• 2008

Let P be a poset and G = G(P) be the incomparability graph of P. Stanley [7] defined the chromatic symmetric function $X_{G(P)}$ which generalizes the chromatic polynomial ${\chi}_G$ of G, and showed all coefficients are nonnegative in the e-expansion of $X_{G(P)}$ for a poset P of rank 1. In this paper, we construct a sign reversing involution on the set of special rim hook P-tableaux with some conditions. It gives a combinatorial proof for (3+1)-free conjecture of a poset P of rank 1.

• Proceedings of the PSK Conference
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• 2003.04a
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• pp.69-71
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• 2003

As recent as 10 years ago, a method of developing new medicine was developed by a new compounding method moving away from an existing one. Combinatorial chemistry made it easier to combine various kinds of compounds in a very short time and with little effort from existing methods. Through combinatorial chemistry, a number of compounds were synthesized using HTS(High Throughput Screening), with many reports reaching a clinical stage in search of new candidate material. (omitted)

• Archives of Pharmacal Research
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• v.27 no.8
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• pp.811-815
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• 2004

Coumarin and its derivatives occur widely in nature. Many attempts were made for synthesis of various coumarin derivatives because of their interesting biological activities. In this study, solid phase synthetic approach of 3-(4-hydroxyphenyl)coumarin was achieved for combinatorial synthesis of substituted 3-phenylcoumarin analogues. Starting from 4-hydroxyphenylacetic acid methyl ester, release of 3-(4-hydroxypnehyl)coumarin from polymer support was accom-plished.

• Proceedings of the Polymer Society of Korea Conference
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• 2006.10a
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• pp.110-111
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• 2006

Most applications of polymers involve blends and mixtures of components including solvents, surfactants, copolymers, fillers, organic or inorganic functional additives, and various processing aids. These components provide unique properties of polymeric materials even beyond those tailored into the basic chemical structures. In addition, skillful processing extends the properties for even greater applications. The perennial challenge of polymer science is to understand and exploit the structure-processing-property interplay relationship. We are developing and demonstrating combinatorial methods and high throughput analysis as tools to provide this fundamental understanding.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.493-503
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• 2014

We consider the simple antisymmetrized algebra $N(e^{A_P},n,t)_1^-$. The simple non-associative algebra and its simple subalgebras are defined in the papers [1], [3], [4], [5], [6], [8], [13]. Some authors found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra in their papers [2], [3], [5], [7], [9], [10], [13], [15], [16]. We find all the derivations of the Lie subalgebra $N(e^{{\pm}x_1x_2x_3},0,3)_{[1]}{^-}$ of $N(e^{A_p},n,t)_k{^-}$ in this paper.