scholarly journals SOME INEQUALITY RELATIONSHIPS CONCERNING POWER SUMS AND THE ELEMENTARY SYMMETRIC FUNCTIONS.

1968 ◽  
Author(s):  
J Hundhausen
Keyword(s):  
Symmetric Functions ◽  
Elementary Symmetric Functions ◽  
Power Sums

Multiplicative relations between coefficients of logarithmic derivatives of 𝔽q-linear functions and applications

2015 ◽  
Vol 14 (09) ◽  
pp. 1540006 ◽  
Author(s):  
José Alejandro Lara Rodríguez ◽  
Dinesh S. Thakur
Keyword(s):  
Power Series ◽  
Function Field ◽  
Symmetric Functions ◽  
Linear Functions ◽  
Linear Forms ◽  
Elementary Symmetric Functions ◽  
Power Sums ◽  
Formal Power ◽  
Derivatives Of ◽  
Logarithmic Derivatives

We prove some interesting multiplicative relations which hold between the coefficients of the logarithmic derivatives obtained in a few simple ways from 𝔽q-linear formal power series. Since the logarithmic derivatives connect power sums to elementary symmetric functions via the Newton identities, we establish, as applications, new identities between important quantities of function field arithmetic, such as the Bernoulli–Carlitz fractions and power sums as well as their multivariable generalizations. Resulting understanding of their factorizations has arithmetic significance, as well as applications to function field zeta and multizeta values evaluations and relations between them. Using specialization/generalization arguments, we provide much more general identities on linear forms providing a switch between power sums for positive and negative powers.

scholarly journals A note on extrema of linear combinations of elementary symmetric functions

2012 ◽  
Vol 60 (2) ◽  
pp. 219-224 ◽  
Author(s):  
Alexander Kovačec ◽  
Salma Kuhlmann ◽  
Cordian Riener
Keyword(s):  
Symmetric Functions ◽  
Linear Combinations ◽  
Elementary Symmetric Functions

scholarly journals Some New Methods in the Theory of $m$-Quasi-Invariants

10.37236/1877 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
J. Bell ◽  
A. M. Garsia ◽  
N. Wallach
Keyword(s):  
Symmetric Functions ◽  
Free Module ◽  
Finitely Generated ◽  
Graded Algebras ◽  
New Approach ◽  
Elementary Symmetric Functions ◽  
New Methods ◽  
Regular Sequences

We introduce here a new approach to the study of $m$-quasi-invariants. This approach consists in representing $m$-quasi-invariants as $N^{tuples}$ of invariants. Then conditions are sought which characterize such $N^{tuples}$. We study here the case of $S_3$ $m$-quasi-invariants. This leads to an interesting free module of triplets of polynomials in the elementary symmetric functions $e_1,e_2,e_3$ which explains certain observed properties of $S_3$ $m$-quasi-invariants. We also use basic results on finitely generated graded algebras to derive some general facts about regular sequences of $S_n$ $m$-quasi-invariants

scholarly journals A Unified View of Determinantal Expansions for Jack Polynomials

10.37236/1547 ◽  
2000 ◽  
Vol 8 (1) ◽  
Author(s):  
Leigh Roberts
Keyword(s):  
Differential Geometry ◽  
Symmetric Functions ◽  
Jack Polynomials ◽  
Elementary Symmetric Functions ◽  
Fundamental Symmetry ◽  
Unified View

Recently Lapointe et. al. [3] have expressed Jack Polynomials as determinants in monomial symmetric functions $m_\lambda$. We express these polynomials as determinants in elementary symmetric functions $e_\lambda$, showing a fundamental symmetry between these two expansions. Moreover, both expansions are obtained indifferently by applying the Calogero-Sutherland operator in physics or quasi Laplace Beltrami operators arising from differential geometry and statistics. Examples are given, and comments on the sparseness of the determinants so obtained conclude the paper.

scholarly journals On the integrality of the first and second elementary symmetric functions of $1, 1/2^{s_2}, ...,1/n^{s_n}$

2017 ◽  
Vol 2 (4) ◽  
pp. 682-691 ◽  
Author(s):  
Wanxi Yang ◽  
◽  
Mao Li ◽  
Yulu Feng ◽  
Xiao Jiang ◽  
...  
Keyword(s):  
Symmetric Functions ◽  
Elementary Symmetric Functions

scholarly journals On some inequalities for elementary symmetric functions

1994 ◽  
Vol 50 (2) ◽  
pp. 317-326 ◽  
Author(s):  
Mi Lin ◽  
Neil S. Trudinger
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symmetric Functions ◽  
Partial Differential ◽  
Elementary Symmetric Functions

In this note, we prove certain inequalities for elementary symmetric funtions that are relevant to the study of partial differential equations associated with curvature problems.

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