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
Famous quotes containing the words ring of, ring and/or functions:
“I saw Eternity the other night,
Like a great ring of pure and endless light,”
—Henry Vaughan (1622–1695)
“The world,—this shadow of the soul, or other me, lies wide around. Its attractions are the keys which unlock my thoughts and make me acquainted with myself. I run eagerly into this resounding tumult. I grasp the hands of those next to me, and take my place in the ring to suffer and to work, taught by an instinct, that so shall the dumb abyss be vocal with speech.”
—Ralph Waldo Emerson (1803–1882)
“When Western people train the mind, the focus is generally on the left hemisphere of the cortex, which is the portion of the brain that is concerned with words and numbers. We enhance the logical, bounded, linear functions of the mind. In the East, exercises of this sort are for the purpose of getting in tune with the unconscious—to get rid of boundaries, not to create them.”
—Edward T. Hall (b. 1914)