In algebra and in particular in algebraic combinatorics, the ring of symmetric functions, is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes to infinity. This ring serves as universal structure in which relations between symmetric polynomials can be expressed in a way independent of the number n of indeterminates (but its elements are neither polynomials nor functions). Among other things, this ring plays an important role in the representation theory of the symmetric groups.
Other articles related to "ring of symmetric functions, functions, of symmetric functions, symmetric functions":
... of R] allows expression the generating functions of several sequences of symmetric functions to be elegantly expressed ... operations taking place in R] but outside its subring ΛR], so they are meaningful only if symmetric functions are viewed as formal power series in indeterminates Xi ... We shall write "(X)" after the symmetric functions to stress this interpretation ...
Famous quotes containing the words functions and/or ring:
“Empirical science is apt to cloud the sight, and, by the very knowledge of functions and processes, to bereave the student of the manly contemplation of the whole.”
—Ralph Waldo Emerson (18031882)
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—Book Of Common Prayer, The. Solemnization of Matrimony, Wedding, (1662)