• 호남수학학술지
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• 제34권4호
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• pp.483-494
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• 2012

The set of all polynomial permutations of $\mathbb{Z}_{p^r}$ forms a group. We investigate the structure of the group and some related groups, and completely determine the structure of the group of all polynomial permutations of $\mathbb{Z}_{p^2}$.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.657-663
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• 2005

In this paper, we consider groups of permutations S on a set A acting on subsets X of A. In particular, we show that if $X_2{\subseteq}X_1{\subseteq}A$ and Y is an S-normal extension of $X_2 in X_1$, then the Galois group $G_{S}(X_1/Y){\;}of{\;}X_1{\;}over{\;}X_2$ relative to S is an S-closed subgroup of $G_{S}(X_1/X_2)$ in the setting of a Galois theory (correspondence) for this situation.

• 정보보호학회논문지
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• 제6권4호
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• pp.97-106
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• 1996

유한체 GF($2^n$)상의 모든 지수 함수들의 군에 동치 관계를 정의하고, 이들 동치 관계에 의해 분류된 각 동치류에 속하는 지수 함수들은 동일한 암호학적 성질을 가짐을 보인다. 그리고, GF($2^7$)과 GF($2^8$)상의 모든 지수 함수들을 분류한다. 다음으로 지수 함수 분류의 3가지 응용을 제시한다. 우선 GF($2^n$)상의 2개의 지수 함수의 연접에 의한 $n\;{\times}\;2n$ S(ubstitution)-box의 설계 방법을 제안하고, 그들의 입.출력 변화 내성과 선형 내성을 분석한다. 그리고, Eurocrypt '93에서 Beth가 세운 가설이 그릇된 것임을 지적하고, LOKI 블록 알고리즘에 사용된 S-box의 안전성에 대하여 논한다.

• 대한수학회보
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• 제53권2호
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• pp.495-506
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• 2016

In this note we consider the monoid $\mathcal{PODI}_n$ of all monotone partial permutations on $\{1,{\ldots},n\}$ and its submonoids $\mathcal{DP}_n$, $\mathcal{POI}_n$ and $\mathcal{ODP}_n$ of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids $\mathcal{POI}_n$ and $\mathcal{ODP}_n$ are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that $\mathcal{PODI}_n$ is a quotient of a semidirect product of $\mathcal{POI}_n$ and the group $\mathcal{C}_2$ of order two and, analogously, $\mathcal{DP}_n$ is a quotient of a semidirect product of $\mathcal{ODP}_n$ and $\mathcal{C}_2$.

• 한국정보처리학회논문지
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• 제4권10호
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• pp.2493-2500
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• 1997

대칭키 관리 시스템에서 계층적 구조를 지닌 다중 사용자 그룹에 대한 새로운 키관리 방안을 제안한다. 제안된 방식은 의사 랜덤치환에 의해 새성되는 트랩도어 일방향 치환을 이용하며, 구현시 시간과 공간적 측면에서 유리하기 때문에, 완전순서 집합과 부분순서가 있는 집합으로 구성되는 다단계 계층적 구조에 사용 가능하다. 또한, 다른 제안 방식과 비교하여 성능을 분석하고, 제안 방식이 키생성 시간과 키저장 크기에서 보다 효율적인 것을 보인다.

• 대한수학회보
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• 제60권3호
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• pp.733-746
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• 2023

Let (X, d) be a semimetric space. A permutation Φ of the set X is a combinatorial self similarity of (X, d) if there is a bijective function f : d(X × X) → d(X × X) such that d(x, y) = f(d(Φ(x), Φ(y))) for all x, y ∈ X. We describe the set of all semimetrics ρ on an arbitrary nonempty set Y for which every permutation of Y is a combinatorial self similarity of (Y, ρ).

• 대한수학회지
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• 제35권1호
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• pp.225-234
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• 1998

We compute genus distributions for bouquets of dipoles by using the method concerning the cycle structure of permutations in the symmetric group. From this, we can deduce that every bouquet of dipoles is upper embeddable. We find a foumula for computing the embedding polynomials for bouquets of dipoles.

• 대한수학회지
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• 제34권2호
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• pp.337-344
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• 1997

In this paper, we study the isomorphism problem of Cayley permutation graphs. We obtain a necessary and sufficient condition that two Cayley permutation graphs are isomrphic by a direction-preserving and color-preserving (positive/negative) natural isomorphism. The result says that if a graph G is the Cayley graph for a group $\Gamma$ then the number of direction-preserving and color-preserving positive natural isomorphism classes of Cayley permutation graphs of G is the number of double cosets of $\Gamma^\ell$ in $S_\Gamma$, where $S_\Gamma$ is the group of permutations on the elements of $\Gamma and \Gamma^\ell$ is the group of left translations by the elements of $\Gamma$. We obtain the number of the isomorphism classes by counting the double cosets.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제5권
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• pp.523-523
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• 1997

Suppose that G is a group of permutations of a set ${\Omega}$. For a finite subset ${\gamma}$of${\Omega}$, the movement of ${\gamma}$ under the action of G is defined as move(${\gamma}$):=$max\limits_{g{\epsilon}G}|{\Gamma}^{g}{\backslash}{\Gamma}|$, and ${\gamma}$ will be said to have restricted movement if move(${\gamma}$)<|${\gamma}$|. Moreover if, for an infinite subset ${\gamma}$of${\Omega}$, the sets|{\Gamma}^{g}{\backslash}{\Gamma}| are finite and bounded as g runs over all elements of G, then we may define move(${\gamma}$)in the same way as for finite subsets. If move(${\gamma}$)${\leq}$m for all ${\gamma}$${\subseteq}$${\Omega}$, then G is said to have bounded movement and the movement of G move(G) is defined as the maximum of move(${\gamma}$) over all subsets ${\gamma}$ of ${\Omega}$. Having bounded movement is a very strong restriction on a group, but it is natural to ask just which permutation groups have bounded movement m. If move(G)=m then clearly we may assume that G has no fixed points is${\Omega}$, and with this assumption it was shown in [4, Theorem 1]that the number t of G=orbits is at most 2m-1, each G-orbit has length at most 3m, and moreover|${\Omega}$|${\leq}$3m+t-1${\leq}$5m-2. Moreover it has recently been shown by P. S. Kim, J. R. Cho and C. E. Praeger in [1] that essentially the only examples with as many as 2m-1 orbits are elementary abelian 2-groups, and by A. Gardiner, A. Mann and C. E. Praeger in [2,3]that essentially the only transitive examples in a set of maximal size, namely 3m, are groups of exponent 3. (The only exceptions to these general statements occur for small values of m and are known explicitly.) Motivated by these results, we would decide what role if any is played by primes other that 2 and 3 for describing the structure of groups of bounded movement.

• Journal of Forest and Environmental Science
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• 제37권1호
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• pp.14-24
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• 2021

A plant community is a group of populations that coexist in space and interact directly or indirectly with the environment. In this paper, we determined the pattern of tree species composition in response to soil variables in Khadimnagar National Park (KNP), which is one of the least studied tropical forests in Bangladesh. Soil and vegetation data were collected from 71 sample plots. Canonical Correspondence Analysis (CCA) with associated Monte Carlo permutation tests (499 permutations) was carried out to determine the most significant soil variable and to explore the relationship between tree species distribution and soil variables. Soil pH and clay content (pH with p<0.01 and Clay content with p<0.05) were the most significant variables that influence the overall tree species distribution in KNP. Soil pH is related to the distribution and abundance of Syzygium grande and Magnolia champaca, which were mostly found and dominant species in KNP. Some species were correlated with clay content such as Artocarpus chaplasha and Cassia siamea. These observations suggest that both the physico-chemical properties of soil play a major role in shaping the tree distribution in KNP. Hence, these soil properties should take into account for any tree conservation strategy in this forest.