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 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

New Methods of Technological Cooperation in Europe

1992 ◽  
Vol 6 (4) ◽  
pp. 229-238
Author(s):  
Helwig Schmied
Keyword(s):  
Basic Assumption ◽  
Research Collaboration ◽  
Management Problem ◽  
New Approach ◽  
New Methods ◽  
Technological Cooperation ◽  
Core Problem ◽  
And Robotics

This article is founded on the basic assumption that Europe taken as a whole possesses all the necessary resources to combat successfully any non-European competitor in the fields of technology, provided that it solves the management problem of organizing the coordination of those resources. At present, the author argues, they are dispersed and so underexploited. To contribute to the solution of this core problem, he sets out a new approach to research collaboration, using the example of the German–French Institute for Automation and Robotics to show ways in which HEIs can cooperate internationally to provide industry with what it needs to be truly competitive.

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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