Notes on particular symmetric polynomials with applications

作者：El Mikkawy Moawwad^*; Sogabe Tomohiro

来源：Applied Mathematics and Computation, 2010, 215(9): 3311-3317.

DOI：10.1016/j.amc.2009.10.019

• Elementary symmetric polynomials
• Complete symmetric polynomials
• Power sum symmetric polynomials
• Matrices
• Determinant
• LU factorization
• Stirling numbers

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.

• 出版日期2010-1-1