• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.917-923
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• 2000

In this paper, we obtain the number of the minimal generalized permutations on a finite set. Also, we determine the minimal generalized permutations on a set X of cardinality less than or equal to 4.

• 대한수학회지
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• 제50권3호
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• pp.529-541
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• 2013

We study 132 avoiding permutations that also avoid $(2r+1)(2r+2){\cdots}12$ but contain $(2r-1)(2r){\cdots}12$ pattern. We find an identity between the number of these permutations and the Narayana number. We also present relations between 132 avoiding permutations and polygon dissections. Finally, a generalization of these permutations is obtained.

• 호남수학학술지
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• 제29권4호
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• pp.495-509
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• 2007

In this note it is proved that MPR is rigid as a Hopf algebra with distinguished basis. I.e. there are no nontrivial automorphisms that preserve the multiplication and comultiplication and take the distinguished basis of all permutations into itself (as a graded set).

• 대한수학회지
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• 제38권4호
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• pp.793-806
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• 2001

In this paper we consider the enumeration problem of permutations with partially forbidden positions, generalizing the notion of permutations with forbidden positions. .As an alternative approach to this problem, we investigate the permanent maximization problem over some classes of (0,1)-matrices which have a given number of 1's some of which lie in prescribed positions.

• 대한수학회지
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• 제54권4호
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• pp.1149-1161
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• 2017

An ($n_1,\;n_2,\;{\ldots},\;n_k$)-colored permutation is a permutation of $n_1+n_2+{\cdots}+n_k$ in which $1,\;2,\;{\ldots},\;n_1$ have color 1, and $n_1+1,\;n_1+2,\;{\ldots},\;n_1+n_2$ have color 2, and so on. We give a bijective proof of Steinhardt's result: the number of colored permutations with no monochromatic cycles is equal to the number of permutations with no fixed points after reordering the first $n_1$ elements, the next $n_2$ element, and so on, in ascending order. We then find the generating function for colored permutations with no monochromatic cycles. As an application we give a new proof of the well known generating function for colored permutations with no fixed colors, also known as multi-derangements.

• 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.

• 충청수학회지
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• 제34권3호
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• pp.253-257
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• 2021

In this paper, we provide a recursive formula for the number of involutions of doubly alternating Baxter permutations in S_n.

• 대한수학회지
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• 제43권3호
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• pp.553-561
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• 2006

In this paper, we give an alternative proof that the number of doubly alternating Baxter permutations is Catalan.

• 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.