• Korean Journal of Mathematics
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• v.22 no.2
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• pp.325-337
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• 2014

In 1911 Schur[6] derived degree and character formulas for projective representations of the symmetric groups remarkably similar to the corresponding formulas for ordinary representations. Morris[3] derived a recurrence for evaluation of spin characters and Stembridge[8] gave a combinatorial reformulation for Morris' recurrence. In this paper we give combinatorial interpretations for the orthogonality relations of spin characters based on Stembridge's combinatorial reformulation for Morris' rule.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1007-1014
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• 2012

We derive the exact reciprocity formula connecting the twisted second moments at 1 for families of odd Dirichlet characters corresponding to two prime moduli, which parallels such formula discovered earlier for the special point 1/2.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.551-563
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• 2002

We Construct a Sign reversing involution on the Shifted rim hook tableaux with some conditions. Using the Stembridge's combinatorial interpretation for Morris' rule, this involution give a combinatorial proof of the orthogonality of the first kind for the spin characters of $S_{n}$.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1497-1522
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• 2023

In this paper we compute the Bredon homology of wallpaper groups with respect to the family of finite groups and with coefficients in the complex representation ring. We provide explicit bases of the homology groups in terms of irreducible characters of the stabilizers.

• Kyungpook Mathematical Journal
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• v.24 no.1
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• pp.1-15
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• 1984

• Journal of the Korean Institute of Telematics and Electronics
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• v.9 no.4
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• pp.25-32
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• 1972

This paper: a) discusses the structure of Korean charactors from a unified point of view. The forming process of vowels, consonants, and the combined characters are described in the same way. b) makes clear that vowels and consonants are unique determinants of combined characters according to speech sound. c) describes the way in which 10 vowels and 14 consonants are arranged systematically by the matrix equation, which forms 14,364 kinds of combined characters.

• The Journal of the Korea institute of electronic communication sciences
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• v.14 no.2
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• pp.433-438
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• 2019

This paper proposes a method of improving deep learning based numbers and characters recognition performance on parts of drawing through image preprocessing. The proposed character recognition system consists of image preprocessing and 7 layer deep learning model. Mathematical morphological filtering is used as preprocessing to remove the lines and shapes which causes false recognition of numbers and characters on parts drawing. Further.. Further, the used deep learning model is a 7 layer deep learning model instead of VGG-16 model. As a result of the proposed OCR method, the recognition rate of characters is 92.57% and the precision is 92.82%.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1221-1230
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• 2018

We derive a sharp decomposition formula for the state polytope of the Hilbert point and the Hilbert-Mumford index of reducible varieties by using the decomposition of characters and basic convex geometry. This proof captures the essence of the decomposition of the state polytopes in general, and considerably simplifies an earlier proof by the authors which uses a careful analysis of initial ideals of reducible varieties.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1037-1049
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• 2018

In this paper, we have first presented the construction of the linear characters of a finite Coxeter group $G_n$ of type $B_n$ by lifting all linear characters of the quotient group $G_n/[G_n,G_n]$ of the commutator subgroup $[G_n,G_n]$. Also we show that the sets of distinguished coset representatives $D_A$ and $D_{A^{\prime}}$ for any two signed compositions A, A' of n which are $G_n$-conjugate to each other and for each conjugate class ${\mathcal{C}}_{\lambda}$ of $G_n$, where ${\lambda}{\in}\mathcal{BP}(n)$, the equality ${\mid}{\mathcal{C}}_{\lambda}{\cap}D_A{\mid}={\mid}{\mathcal{C}}_{\lambda}{\cap}D_{A^{\prime}}{\mid}$ holds. Finally, we have given the general structure of units of Mantaci-Reutenauer algebra.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2095-2105
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• 2015

Given c, a positive integer, we set. $$M(f,c):=\frac{2}{{\phi}(f)}\sum_{{\chi}{\in}X^-_f}{\chi}(c)|L(1,{\chi})|^2$$, where $X^-_f$ is the set of the $\phi$(f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f's such that their prime divisors are all equal to ${\pm}1$ modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c $\in$ {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.