• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.789-796
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• 1997

We consider a Pfaffian and its combinatorial model. We give a bijection between Pfaffian and the generating function of weights of generalized Young tableaux by this combinatorial model, and we find an explicit formula for the Pfaffian by this bijection.

• East Asian mathematical journal
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• v.37 no.1
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• pp.1-7
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• 2021

In modern block ciphers, S-box plays a very important role in the secrets of symmetric encryption algorithms. Many popular block ciphers have adopted various S-Boxes to design better S-Boxes. Among the researches, Jin et al. proposed a simple scheme to create a new S-box from Rijndael S-box. Only one of the new S-boxes for 29 is a bijection with a better algebraic representation than the original. Therefore, they asked a few questions. In this paper, we answer the following question : When the resulting S-box is bijection?

• 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 $P_{n}$ . .

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.963-986
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• 2022

Given a dimension function 𝜔, we introduce the notion of an 𝜔-vector weighted digraph and an 𝜔-equivalence between them. Then we establish a bijection between the weakly (ℤ/2)ⁿ-equivariant homeomorphism classes of small covers over a product of simplices ∆^𝜔(1) × ⋯ × ∆^𝜔(m) and the set of 𝜔-equivalence classes of 𝜔-vector weighted digraphs with m-labeled vertices, where n is the sum of the dimensions of the simplicies. Using this bijection, we obtain a formula for the number of weakly (ℤ/2)ⁿ-equivariant homeomorphism classes of small covers over a product of three simplices.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.245-248
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• 2009

We consider pm-ring with the property such that every prime ideal is contained in only one maximal ideal. Orsatti[4] characterized pm-rings by means of the retraction. Contessa[1] found algebraic condition, by using that direct product of pm-rings is a pm-ring. We show that C(X, H) and C(X, C) are pm-rings and we extend a quasi pm-domain.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.265-277
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• 1997

Let E be a real, non-degenerate, indefinite inner product space with dim $E \geq 3$. It is shown that any bijection of E which preserves the light cones is an affine map.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.1-7
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• 2016

Some properties of filters are studied with respect to a congru-ence of BE-algebras. The notion of θ-filters is introduced and these classes of filters are then characterized in terms of congruence classes. A bijection is obtained between the set of all θ-filters of a BE-algebra and the set of all filters of the respective BE-algebra of congruences classes.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1883-1891
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• 2017

An optimally labelled graph of bandwidth 2 is an ordered pair (G, f) where G is a simple graph with bw(G) = 2 and $f:V(G){\rightarrow}[n]$ is a bijection such that bw(G, f) = 2. In this paper, the number of optimally labelled graphs of bandwidth two of order n is enumerated by counting linear forests.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.901-914
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• 1999

In [6] Schensted constructed the Schensted algorithm giving a bijection between permutations and pairs of Young standard tableaux. After knuth generalized it to column strict tableaux in [3] various analogs of the Schensted algorithm came. In this paper we describe the bumping algorithm on the shifted rim hook tableaux which is the basic building block of the Schensted algorithm for shifted rim book tableaux.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.289-309
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• 2014

A combinatorial description of the crystal $\mathcal{B}({\infty})$ for finite-dimensional simple Lie algebras in terms of certain Young tableaux was developed by J. Hong and H. Lee. We establish an explicit bijection between these Young tableaux and canonical bases indexed by Lusztig's parametrization, and obtain a combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum over the set of Young tableaux.