scholarly journals The Schur Harmonic Convexity of the Hamy Symmetric Function and Its Applications

2009 ◽  
Vol 2009 (1) ◽  
pp. 838529 ◽  
Author(s):  
Yuming Chu ◽  
Yupei Lv
Keyword(s):  
Symmetric Function ◽  
Harmonic Convexity

scholarly journals A Reverse Analytic Inequality for the Elementary Symmetric Function with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Huan-Nan Shi ◽  
Jing Zhang
Keyword(s):  
Symmetric Function ◽  
Elementary Symmetric Function ◽  
Dimensional Simplex ◽  
Reverse Inequality ◽  
Convexity Theory ◽  
Harmonic Convexity

We give a reverse inequality involving the elementary symmetric function by use of the Schur harmonic convexity theory. As applications, several new analytic inequalities for then-dimensional simplex are established.

Corrigenda to “On Non-Compact Operators in Weighted Ideal and Symmetric Function Spaces”

2007 ◽  
Vol 14 (4) ◽  
pp. 807-808
Author(s):  
Giorgi Oniani
Keyword(s):  
Symmetric Function ◽  
Compact Operators ◽  
Function Spaces ◽  
J 13

Abstract Corrections to [Oniani, Georgian Math. J. 13: 501–514, 2006] are listed.

The Schur multiplicative and harmonic convexities of the complete symmetric function

2011 ◽  
Vol 284 (5-6) ◽  
pp. 653-663 ◽  
Author(s):  
Y.-M. Chu ◽  
G.-D. Wang ◽  
X.-H. Zhang
Keyword(s):  
Symmetric Function ◽  
Complete Symmetric Function

The Hammond Series of a Symmetric Function and Its Application to P-Recursiveness

1983 ◽  
Vol 4 (2) ◽  
pp. 179-193 ◽  
Author(s):  
I. P. Goulden ◽  
D. M. Jackson ◽  
J. W. Reilly
Keyword(s):  
Symmetric Function

scholarly journals How to get the weak order out of a digraph ?

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Francois Viard
Keyword(s):  
Wreath Product ◽  
Symmetric Function ◽  
Coxeter Groups ◽  
Symmetric Functions ◽  
Weak Order ◽  
Möbius Function ◽  
Mobius Function ◽  
Acyclic Digraph ◽  
International Audience

International audience We construct a poset from a simple acyclic digraph together with a valuation on its vertices, and we compute the values of its Möbius function. We show that the weak order on Coxeter groups $A$<sub>$n-1$</sub>, $B$<sub>$n$</sub>, $Ã$<sub>$n$</sub>, and the flag weak order on the wreath product &#8484;<sub>$r$</sub> &#8768; $S$<sub>$n$</sub> introduced by Adin, Brenti and Roichman (2012), are special instances of our construction. We conclude by briefly explaining how to use our work to define quasi-symmetric functions, with a special emphasis on the $A$<sub>$n-1$</sub> case, in which case we obtain the classical Stanley symmetric function. On construit une famille d’ensembles ordonnés à partir d’un graphe orienté, simple et acyclique munit d’une valuation sur ses sommets, puis on calcule les valeurs de leur fonction de Möbius respective. On montre que l’ordre faible sur les groupes de Coxeter $A$<sub>$n-1$</sub>, $B$<sub>$n$</sub>, $Ã$<sub>$n$</sub>, ainsi qu’une variante de l’ordre faible sur les produits en couronne &#8484;<sub>$r$</sub> &#8768; $S$<sub>$n$</sub> introduit par Adin, Brenti et Roichman (2012), sont des cas particuliers de cette construction. On conclura en expliquant brièvement comment ce travail peut-être utilisé pour définir des fonction quasi-symétriques, en insistant sur l’exemple de l’ordre faible sur $A$<sub>$n-1$</sub> où l’on obtient les séries de Stanley classiques.

scholarly journals A Quasisymmetric Function Generalization of the Chromatic Symmetric Function

10.37236/518 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Brandon Humpert
Keyword(s):  
Symmetric Function ◽  
Chromatic Polynomial ◽  
Quasisymmetric Function ◽  
Quasisymmetric Functions ◽  
Acyclic Orientations ◽  
Chromatic Symmetric Function

The chromatic symmetric function $X_G$ of a graph $G$ was introduced by Stanley. In this paper we introduce a quasisymmetric generalization $X^k_G$ called the $k$-chromatic quasisymmetric function of $G$ and show that it is positive in the fundamental basis for the quasisymmetric functions. Following the specialization of $X_G$ to $\chi_G(\lambda)$, the chromatic polynomial, we also define a generalization $\chi^k_G(\lambda)$ and show that evaluations of this polynomial for negative values generalize a theorem of Stanley relating acyclic orientations to the chromatic polynomial.

Inequalities for Generalized Symmetric Functions

1969 ◽  
Vol 12 (5) ◽  
pp. 615-623 ◽  
Author(s):  
K.V. Menon
Keyword(s):  
Symmetric Function ◽  
Symmetric Functions ◽  
Elementary Symmetric Function ◽  
Generating Series ◽  
Image Position ◽  
Complete Symmetric Function

The generating series for the elementary symmetric function Er, the complete symmetric function Hr, are defined byrespectively.

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