Notes on particular symmetric polynomials with applications
نویسندگان
چکیده
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. 2009 Elsevier Inc. All rights reserved.
منابع مشابه
Buckling and vibration analysis of angle -ply symmetric laminated composite plates with fully elastic boundaries
The main focus of this paper is on efficiency analysis of two kinds of approximating functions (characteristic orthogonal polynomials and characteristic beam functions) that have been applied in the Rayleigh-Ritz method to determine the non-dimensional buckling and frequency parameters of an angle ply symmetric laminated composite plate with fully elastic boundaries. It has been observed that o...
متن کاملOn Matrix Polynomials with Real Roots
It is proved that the roots of combinations of matrix polynomials with real roots can be recast as eigenvalues of combinations of real symmetric matrices, under certain hypotheses. The proof is based on recent solution of the Lax conjecture. Several applications and corollaries, in particular concerning hyperbolic matrix polynomials, are presented.
متن کاملTraceless Symmetric Tensor Approach to Legendre Polynomials and Spherical Harmonics
In these notes I will describe the separation of variable technique for solving Laplace’s equation, using spherical polar coordinates. The solutions will involve Legendre polynomials for cases with azimuthal symmetry, and more generally they will involve spherical harmonics. I will construct these solutions using traceless symmetric tensors, but in Lecture Notes 8 I describe how the solutions i...
متن کاملIntroductions to Symmetric Polynomials and Symmetric Functions
Symmetric polynomials and symmetric functions are ubiquitous in mathematics and mathematical physics. For example, they appear in elementary algebra (e.g. Viete’s Theorem), representation theories of symmetric groups and general linear groups over C or finite fields. They are also important objects to study in algebraic combinatorics. Via their close relations with representation theory, the th...
متن کاملSymmetry classes of polynomials associated with the dihedral group
In this paper, we obtain the dimensions of symmetry classes of polynomials associated with the irreducible characters of the dihedral group as a subgroup of the full symmetric group. Then we discuss the existence of o-basis of these classes.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 215 شماره
صفحات -
تاریخ انتشار 2010