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.

Read more about Ring Of Symmetric Functions: Symmetric Polynomials, The Ring of Symmetric Functions

### Other articles related to "ring of symmetric functions, functions, of symmetric functions, symmetric functions":

**Ring Of Symmetric Functions**- Properties of The

**Ring of Symmetric Functions**- Generating Functions

... The first definition of ΛR as a subring of R] allows expression the generating

**functions**of several sequences

**of symmetric functions**to be elegantly expressed ... 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 (1803–1882)

“The boxer’s *ring* is the enjoyment of the part of society whose animal nature alone has been developed.”

—Ralph Waldo Emerson (1803–1882)