• Honam Mathematical Journal
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• v.26 no.3
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• pp.257-268
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• 2004

In this paper, we give a proof of the Robinson-Schensted-Knuth correspondence by using the geometric. construction. We represent a generalized permutation in the first quadrant of the Cartesian plane and find a corresponding pair of semi-standard tableaux of same shape. This work extends the classical geometric construction of Viennot [10] for Robinson-Schensted correspondence.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.921-948
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• 2021

We continue the investigations in [6] extending the Bruhat order on n × n alternating sign matrices to our more general setting. We show that the resulting partially ordered set is a graded lattice with a well-define rank function. Many illustrative examples are given.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.445-459
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• 1998

Let λ be a partition with all distinct parts. In this paper we give a bijection between the set $\Gamma$$_{λ}$(X) of pairs (equation omitted) satisfying a certain condition and the set $\pi_{λ}$(X) of circled permutation tableaux of shape λ on the set X, where P$\frac{1}{2}$ is a tail circled shifted rim hook tableaux of shape λ and (equation omitted) is a barred permutation on X. Specializing to the partition λ with one part, this bijection gives a combinatorial proof of the Schur identity: $\Sigma$2$\ell$(type($\sigma$)) = 2n! summed over all permutation $\sigma$ $\in$ $S_{n}$ with type($\sigma$) $\in$ O $P_{n}$ . .

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2660-2679
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• 2017

Crypton is a SP-network block cipher that attracts much attention because of its excellent performance on hardware. Based on Crypton, mCrypton is designed as a lightweight block cipher suitable for Internet of Things (IoT) and Radio Frequency Identification (RFID). The security of Crypton and mCrypton under meet-in-the-middle attack is analyzed in this paper. By analyzing the differential properties of cell permutation, several differential characteristics are introduced to construct generalized ${\delta}-sets$. With the usage of a generalized ${\delta}-set$ and differential enumeration technique, a 6-round meet-in-the-middle distinguisher is proposed to give the first meet-in-the-middle attack on 9-round Crypton-192 and some improvements on the cryptanalysis of 10-round Crypton-256 are given. Combined with the properties of nibble permutation and substitution, an improved meet-in-the-middle attack on 8-round mCrypton is proposed and the first complete attack on 9-round mCrypton-96 is proposed.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.42 no.8 s.338
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• pp.1-10
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• 2005

In this paper, the explicit low density codes construction from the generalized permutation matrices related to algebra theory is investigated, and we design several Jacket inverse block matrices on the recursive formula and permutation matrices. The results show that the proposed scheme is a simple and fast way to obtain the low density codes, and we also Proved that the structured low density parity check (LDPC) codes, such as the $\pi-rotation$ LDPC codes are the low density Jacket inverse block matrices too.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.303-309
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• 1995

Many measures to detect multicollinearity in linear regression have been proposed in statistics and numerical analysis literature. Among them, condition number and variance inflation factor(VIF) are most popular. In this study, we give new interpretations of condition number and VIF in linear regression, using geometry on the explanatory space. In the same line, we derive natural measures of condition number and VIF for logistic regression. These computer intensive measures can be easily extended to evaluate multicollinearity in generalized linear models.

• The Korean Journal of Applied Statistics
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• v.25 no.5
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• pp.821-827
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• 2012

In this study, we propose a new nonparametric test procedure for the multivariate data. In order to accommodate the generalized alternatives for the multivariate case, we construct test statistics via-values with some useful combining functions. Then we illustrate our procedure with an example and compare efficiency among the combining functions through a simulation study. Finally we discuss some interesting features related with the new nonparametric test as concluding remarks.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.469-487
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• 2016

In [6] Schensted constructed the Schensted algorithm, which gives a bijection between permutations and pairs of standard tableaux of the same shape. Stanton and White [8] gave analog of the Schensted algorithm for rim hook tableaux. In this paper we give a generalization of Stanton and White's Schensted algorithm for rim hook tableaux. If k is a fixed positive integer, it shows a one-to-one correspondence between all generalized hook permutations $\mathcal{H}$ of size k and all pairs (P, Q), where P and Q are semistandard k-rim hook tableaux and k-rim hook tableaux of the same shape, respectively.

• Proceedings of the KIEE Conference
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• 1987.07a
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• pp.185-189
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• 1987

An analysis and design of large-scale linear multivariable systems often requires to be block triangularized form for good sensitivity of the systems when their poles and zeros are varied. But the decomposition algorithms presented up to now need a procedure of permutation, rescaling and a solution of nonlinear algebraic equations, which are usually burden. To avoid these problem, in this paper we develop a newly alternative block triangular decomposition algorithm which used the generalized matrix sign function on the Z-plane. Also, the decomposition algorithm demonstrated using the fifth order linear model of a distillation tower system.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.371-384
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• 2022

Fix an integer n ≥ 1. Then the simplex Π_n, Birkhoff polytope Ω_n, and Latin square polytope Λ_n each yield projective geometries obtained by identifying antipodal points on a sphere bounding a ball centered at the barycenter of the polytope. We investigate conditions for homogeneous coordinates of points in the projective geometries to locate exact vertices of the respective polytopes, namely crisp distributions, permutation matrices, and quasigroups or Latin squares respectively. In the latter case, the homogeneous conditions form a crucial part of a recent projective-geometrical approach to the study of orthogonality of Latin squares. Coordinates based on the barycenter of Ω_n are also suited to the analysis of generalized doubly stochastic matrices, observing that orthogonal matrices of this type form a subgroup of the orthogonal group.