Notes on particular symmetric polynomials with applications |
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| Authors: | Moawwad El-Mikkawy Tomohiro Sogabe |
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| Affiliation: | a Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
b Graduate School of Information Science and Technology, Aichi Prefectural University, 1522-3 Kumabari, Nagakute, Aichi 480-1198, Japan |
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| Abstract: | This paper presents some applications using several properties of three important symmetric polynomials: elementary symmetric polynomials, complete symmetric polynomials and the power sum symmetric polynomials. The applications includes a simple proof of El-Mikkawy conjecture in [M.E.A. El-Mikkawy, Appl. Math. Comput. 146 (2003) 759-769] and a very easy proof of the Newton-Girard formula. In addition, a generalization of Stirling numbers is obtained. |
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| Keywords: | Elementary symmetric polynomials Complete symmetric polynomials Power sum symmetric polynomials Matrices Determinant LU factorization Stirling numbers |
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