Homogeneous Symmetric Polynomial Geometric Inequalities

1989 ◽  
pp. 37-48
Author(s):  
D. S. Mitrinović ◽  
J. E. Pečarić ◽  
V. Volenec
Keyword(s):  
Symmetric Polynomial ◽  
Geometric Inequalities ◽  
Homogeneous Symmetric Polynomial

scholarly journals An Orthosymplectic Pieri Rule

10.37236/7387 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Anna Stokke
Keyword(s):  
Linear Combination ◽  
Schur Functions ◽  
Symmetric Polynomial ◽  
Schur Function ◽  
Product Rule ◽  
Integer Coefficients ◽  
Pieri Formula ◽  
Symplectic Characters ◽  
Homogeneous Symmetric Polynomial

The classical Pieri formula gives a combinatorial rule for decomposing the product of a Schur function and a complete homogeneous symmetric polynomial as a linear combination of Schur functions with integer coefficients. We give a Pieri rule for describing the product of an orthosymplectic character and an orthosymplectic character arising from a one-row partition. We establish that the orthosymplectic Pieri rule coincides with Sundaram's Pieri rule for symplectic characters and that orthosymplectic characters and symplectic characters obey the same product rule. 

scholarly journals Enumerations for Compositions and Complete Homogeneous Symmetric Polynomial

2015 ◽  
Vol 7 (2) ◽  
pp. 1
Author(s):  
Soumendra Bera
Keyword(s):  
Positive Integer ◽  
Symmetric Polynomial ◽  
Enumeration Problems ◽  
Homogeneous Symmetric Polynomial

<p class="abstract">We count the number of occurrences of <em>t </em>as the summands<em> </em>(i) in the compositions of a positive integer <em>n</em> into <em>r</em> parts; and (ii) in all compositions of <em>n</em>; and subsequently obtain other results involving compositions. The initial counting further helps to solve the enumeration problems for complete homogeneous symmetric polynomial.</p>

scholarly journals Pairs of Comparable Relations for Complete Homogeneous Symmetric Polynomial

2015 ◽  
Vol 7 (4) ◽  
pp. 26
Author(s):  
Soumendra Bera
Keyword(s):  
Exponential Function ◽  
Stirling Numbers ◽  
Binomial Coefficient ◽  
Symmetric Polynomial ◽  
Elementary Symmetric Polynomial ◽  
Generating Series ◽  
Homogeneous Symmetric Polynomial

<p>Complete homogeneous symmetric polynomial has connections with binomial coefficient, composition, elementary symmetric polynomial, exponential function, falling factorial, generating series, odd prime and Stirling numbers of the second kind by different summations. Surprisingly the relations in the context are comparable in pairs. </p>

Semimartingales and geometric inequalities on manifolds

2007 ◽  
Vol 75 (2) ◽  
pp. 522-544 ◽  
Author(s):  
Huiling Le ◽  
Dennis Barden
Keyword(s):  
Geometric Inequalities

scholarly journals A Variational Formulation for Dirac Operators in Bounded Domains. Applications to Spectral Geometric Inequalities

2021 ◽  
Author(s):  
Pedro R. S. Antunes ◽  
Rafael D. Benguria ◽  
Vladimir Lotoreichik ◽  
Thomas Ourmières-Bonafos
Keyword(s):  
Variational Formulation ◽  
Dirac Operators ◽  
Bounded Domains ◽  
Geometric Inequalities

scholarly journals Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

2007 ◽  
Vol 79 (4) ◽  
pp. 563-575 ◽  
Author(s):  
Jaume Llibre ◽  
Marcelo Messias
Keyword(s):  
Large Amplitude ◽  
Symmetric Polynomial ◽  
The Other ◽  
Poincaré Compactification ◽  
Heteroclinic Loop ◽  
Differential Systems ◽  
Heteroclinic Cycles ◽  
Polynomial Differential Systems ◽  
Global Study ◽  
Straight Lines

In this paper we study a class of symmetric polynomial differential systems in R³, which has a set of parallel invariant straight lines, forming degenerate heteroclinic cycles, which have their two singular endpoints at infinity. The global study near infinity is performed using the Poincaré compactification. We prove that for all n <FONT FACE=Symbol>Î</FONT> N there is epsilonn > 0 such that for 0 < epsilon < epsilonn the system has at least n large amplitude periodic orbits bifurcating from the heteroclinic loop formed by the two invariant straight lines closest to the x-axis, one contained in the half-space y > 0 and the other in y < 0.

Note on roots location of a symmetric polynomial with respect to the imaginary axis

2012 ◽  
Vol 60 (4) ◽  
pp. 499-510
Author(s):  
Hui-Feng Hao ◽  
Yong-Jian Hu ◽  
Gong-Ning Chen
Keyword(s):  
Imaginary Axis ◽  
Symmetric Polynomial
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