scholarly journals Bernstein operators and super-Schur functions: combinatorial aspects

2018 ◽  
Vol 109 (6) ◽  
pp. 1303-1342
Author(s):  
L. Alarie-Vézina ◽  
O. Blondeau-Fournier ◽  
L. Lapointe ◽  
P. Mathieu
Keyword(s):  
Schur Functions ◽  
Bernstein Operators

scholarly journals CODES AND SHIFTED CODES

2012 ◽  
Vol 22 (06) ◽  
pp. 1250054
Author(s):  
J. T. HIRD ◽  
NAIHUAN JING ◽  
ERNEST STITZINGER
Keyword(s):  
Algebraic Structure ◽  
Schur Functions ◽  
Natural Setting ◽  
Bernstein Operators ◽  
Combinatorial Model

The action of the Bernstein operators on Schur functions was given in terms of codes by Carrell and Goulden (2011) and extended to the analog in Schur Q-functions in our previous work. We define a new combinatorial model of extended codes and show that both of these results follow from a natural combinatorial relation induced on codes. The new algebraic structure provides a natural setting for Schur functions indexed by compositions.

scholarly journals CODES AND SHIFTED CODES OF PARTITIONS

2011 ◽  
Vol 21 (08) ◽  
pp. 1447-1462 ◽  
Author(s):  
J. T. HIRD ◽  
NAIHUAN JING ◽  
ERNEST STITZINGER
Keyword(s):  
Classical Result ◽  
Schur Functions ◽  
Combinatorial Identity ◽  
Bernstein Operators ◽  
Pieri Rules ◽  
Straightforward Consequence

In a recent paper, Carrell and Goulden found a combinatorial identity of the Bernstein operators that they then used to prove Bernstein's theorem. We show that this identity is a straightforward consequence of the classical result. We also show how a similar approach using the codes of partitions can be generalized from Schur functions to also include Schur Q-functions and derive the combinatorial formulation for both cases. We then apply them by examining the Littlewood–Richardson and Pieri rules.

Optimal Assembly of Systems Using Schur-Functions and Majorization.

1986 ◽  
Author(s):  
Emad El-Neweihi ◽  
Frank Proschan ◽  
Jayaram Sethuraman
Keyword(s):  
Schur Functions ◽  
Optimal Assembly

scholarly journals Lupaş type Bernstein operators on triangles based on quantum analogue

2021 ◽  
Vol 60 (6) ◽  
pp. 5909-5919
Author(s):  
Asif Khan ◽  
M.S. Mansoori ◽  
Khalid Khan ◽  
M. Mursaleen
Keyword(s):  
Bernstein Operators ◽  
Quantum Analogue

scholarly journals The Rate of Convergence of Lupasq-Analogue of the Bernstein Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Heping Wang ◽  
Yanbo Zhang
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Bernstein Operators ◽  
Lipschitz Continuous Functions ◽  
Lipschitz Continuous

We discuss the rate of convergence of the Lupasq-analogues of the Bernstein operatorsRn,q(f;x)which were given by Lupas in 1987. We obtain the estimates for the rate of convergence ofRn,q(f)by the modulus of continuity off, and show that the estimates are sharp in the sense of order for Lipschitz continuous functions.

scholarly journals Proof of a positivity conjecture on Schur functions

2013 ◽  
Vol 120 (3) ◽  
pp. 644-648 ◽  
Author(s):  
William Y.C. Chen ◽  
Anne X.Y. Ren ◽  
Arthur L.B. Yang
Keyword(s):  
Schur Functions
Sign in / Sign up

Export Citation Format

Share Document