• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.55-72
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• 2000

In this paper, we develop the Grobner-Shirshov basis theory for the representations of associative algebras by introducing the notion of Grobner-Shirshov pairs. Our result can be applied to solve the reduction problem in representation theory and to construct monomial bases of representations of associative algebras. As an illustration, we give an explicit construction of Grobner-Shirshov pairs and monomial bases for finite dimensional irreducible representations of the simple tie algebra sl$_3$. Each of these monomial bases is in 1-1 correspondence with the set of semistandard Young tableaux with a given shape.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.711-725
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• 2008

We give an explicit construction of Grobner-Shirshov pairs and monomial bases for finite-dimensional irreducible representations of the simple Lie algebra $sp_4$. We also identify the monomial basis consisting of the reduced monomials with a set of semistandard tableaux of a given shape, on which we give a colored oriented graph structure.

• Review of KIISC
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• v.5 no.2
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• pp.26-31
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• 1995

본 논문에서는 다항식 환 k($x_1$,…, $x_n$)에서의 Grobner bases 개념과 응용을 소개하고 있다. 특히 Grobner bases를 이용한 binary cyclic code에 대한 효율적인 algebraic decoding method를 자세히 설명하고 있다.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.595-601
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• 1997

Let $C_d$ be the rational curve of degree d in $P_k ^3$ given parametrically by $x_0 = u^d, X_1 = u^{d - 1}t, X_2 = ut^{d - 1}, X_3 = t^d (d \geq 4)$. Then the defining ideal of $C_d$ can be minimally generated by d polynomials $F_1, F_2, \ldots, F_d$ such that $degF_1 = 2, degF_2 = \cdots = degF_d = d - 1$ and $C_d$ is a set-theoretically complete intersection on $F_2 = X_1^{d-1} - X_2X_0^{d-2}$ for every field k of characteristic p > 0. For the proofs we will use the notion of Grobner basis.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.347-354
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• 2002

An n-point design is maximal fan if all the models with n-terms satisfying the divisibility condition are estimable. Such designs tend to be space filling and look very similar to the ″Latin-hypercube″ designs used in computer experiments. Caboara, Pistone, Riccomago and Wynn (1997) conjectured that a maximal fan design on an integer grid exists for any n and m, where m is the number of factors. In this paper we examine the relationship between maximal fan design and latin-hypercube to give a partial solution for the conjecture.