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Symmetric Functions and Symmetric Species

, 1986
Publisher Summary This chapter introduces the notion of symmetric species, which can be viewed as a set-theoretic (a category-theoretic) counterpart of the notion of a symmetric function. To each of the classical classes of symmetric functions, the chapter associates a symmetric species.
BONETTI F., ROTA G. C., SENATO D, VENEZIA, Antonietta   +3 more
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On Multivalued Symmetric Functions

IEEE Transactions on Computers, 1972
This note describes an algorithm for identifying multivalued symmetric switching functions using parallel processing. Some general properties of multivalued symmetric functions have been investigated. The mixed multivalued symmetric switching function is defined and an algorithm for identifying it is also presented.
Samuel C. Lee, Edward T. Lee
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Singular Symmetric Functionals

Journal of Mathematical Sciences, 2004
The inspiration for the results of this paper is the theorm of \textit{J.~Dixmier} [C.\ R.\ Acad.\ Sci., Paris, Sér.~A 262, 1107--1108 (1966; Zbl 0141.12902)] that there exist nonnormal traces on the von Neumann factor \(B(H)\) which are singular in the sense that they vanish on all finite rank operators.
Dodds, P., de Pagter, B., Sedaev, A., Semenov, E., Sukochev, F.   +4 more
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ON THE MINIMIZATION OF SYMMETRIC FUNCTIONALS

Reviews in Mathematical Physics, 1994
The scope of the present paper is to further develop the method of competing symmetries so that it may be used to solve minimization problems with less symmetry. Emphasis is given to problems for which the invariant submanifold of the flow, to which the search for minimizers can be restricted, is still infinite dimensional.
Carlen, Eric A., Loss, Michael
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On Complete Symmetric Functions

SIAM Journal on Mathematical Analysis, 1988
This paper is devoted to the study of properties of complete symmetric functions playing an important role in the theory of partitions and in combinatorics. Especially the representation and recursive formulas and inequalities involving functions in question are given. The theory is accompanied by some applications.
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Differential Symmetric Functions

Annals of Combinatorics, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Symmetric Functions

1995
Abstract Many of the objects we shall consider in this book will turn out to be parametrized by partitions. The purpose of this section is to lay down some notation and terminology which will be used throughout, and to collect together some elementary results on orderings of partitions which will be used later.
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Properties of Symmetric Fitness Functions

IEEE Transactions on Evolutionary Computation, 2006
The properties of symmetric fitness functions are investigated. We show that the search spaces obtained from symmetric functions have the zero-correlation structures between fitness and distance. It is also proven that symmetric functions induce a class of the hardest problems in terms of the epistasis variance and its variants.
Sung-Soon Choi, Yung-Keun Kwon, Byung Ro Moon   +2 more
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The q-deformation of symmetric functions and the symmetric group

Journal of Physics A: Mathematical and General, 1991
Summary: The \(q\)-deformation of symmetric functions is introduced leading to \(q\)- analogues of many well-known relationships in the theory of symmetric functions, \(q\)-deformed scalar products are developed and used to define \(q\)-dependent symmetric functions.
Salam, M. A., Wybourne, B. G.
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On MacDonald's Symmetric Functions

Bulletin of the London Mathematical Society, 1992
An algorithm for computing Macdonald's two-parameter symmetric functions is suggested. A transition matrix from the basis of power sums to the basis of Macdonald's functions is constructed recursively (with respect to the dominance partial order on partitions) by a method analogous to Shoji's method of computing the Green functions of \(\text{GL}(n,q)\)
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