• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.121-127
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• 1999

We can get the Pascal's matrix of order n by taking the first n rows of Pascal's triangle and filling in with 0's on the right. In this paper we obtain some well known combinatorial identities and a factorization of the Stirling matrix from the Pascal's matrix.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.479-491
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• 2008

In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.413-427
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• 2020

In this work we study 0-commuting matrix C(0) under relationships with the Pascal matrix C(1). Like kth power C(1)k is an arithmetic matrix of (kx+y)n with yx = xy (k ≥ 1), we express C(0)k as an arithmetic matrix of certain polynomial with yx = 0.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.2
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• pp.65-76
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• 2023

With the Stirling matrix S of the second kind and the Pascal matrix T, we study recurrence rules and sequences of certain sums over the matrix ST^k. We find a matrix E satisfying ST = ES and interrelations of S and the Stirling matrix of the first kind.

• East Asian mathematical journal
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• v.40 no.3
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• pp.329-339
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• 2024

In the work we generate arithmetic matrix P^(c,b,a) of (cx² + bx+a)ⁿ from a Pascal matrix P^(1,1). We extend an identity P^(1,1))O^(1,1) = P^(1,1,1) with an obtuse matrix O^(1,1) to k degree polynomials. For the purpose we study P^(1,1)kO^(1,1) and find generating polynomials of O^(1,1)k.

• The Mathematical Education
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• v.43 no.4
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• pp.391-398
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• 2004

It is well-known in the literature that the general term of a sequence can be represented by a linear combination of binomial coefficients. The theorem and its known proofs are not easy for highschool students to understand. In this paper we prove the theorem by a pictorial method and by a very short and easy inductive method to make the problem easy and accessible enough for highschool students.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.26-35
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• 2022

In this paper we introduce two type of representations of the Pascal matrix via induced transformations of some q-derivatives as well as their some combinatorial applications.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.533-546
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• 2020

Since Sheffer introduced the so-called Sheffer polynomials in 1939, the polynomials have been extensively investigated, applied and classified. In this paper, by using matrix algebra, specifically, some properties of Pascal and Wronskian matrices, we aim to present certain interesting identities involving the 2-variable truncated exponential based Sheffer polynomial sequences. Also, we use the main results to give some interesting identities involving so-called 2-variable truncated exponential based Miller-Lee type polynomials. Further, we remark that a number of different identities involving the above polynomial sequences can be derived by applying the method here to other combined generating functions.

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.255-258
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• 2009

It is well known that for a sequence a = ($a_0,\;a_1$,...) the general term of the dual sequence of a is $a_n\;=\;c_0\;^n_0\;+\;c_1\;^n_1\;+\;...\;+\;c_n\;^n_n$, where c = ($c_0,...c_n$ is the dual sequence of a. In this paper, we find the general term of the sequence ($c_0,\;c_1$,... ) and give another method for finding the inverse matrix of the Pascal matrix. And we find a simple proof of the fact that if the general term of a sequence a = ($a_0,\;a_1$,... ) is a polynomial of degree p in n, then ${\Delta}^{p+1}a\;=\;0$.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.10a
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• pp.50-50
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• 1993

이 연구는 선형계획법을 위하여 개발된 프로그램들의 언어 및 자료 구조에 대한 차이를 비교, 분석하고자 한다. 선형계획법을 위하여 사용된 언어로는 C, PASCAL, FORTRAN이 있고 자료구조로는 Full Matrix형태와 Non-Zero Matrix형태를 고려한다. Non-Zero Matrix에서는 프로그램 언어별로 Cursor-Based System을 비교하고자 한다. 위의 실험을 수행하기 위하여 다음의 연구과정을 수행한다. 첫째, Non-Zero Matrix의 이용을 위한 Cursor-Based System과 Pointer-Based System을 설계한다. 둘째, LP프로그램을 위한 Full Matrix와 Non-Zero Matrix의 효율적인 자료구조를 구축한다. 세째, 프로그램 언어와 자료구조별로 LP프로그램의 성능을 비교분석한다.