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":
... 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 ... 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:
“In todays world parents find themselves at the mercy of a society which imposes pressures and priorities that allow neither time nor place for meaningful activities and relations between children and adults, which downgrade the role of parents and the functions of parenthood, and which prevent the parent from doing things he wants to do as a guide, friend, and companion to his children.”
—Urie Bronfenbrenner (b. 1917)
“Full fathom five thy father lies,
Of his bones are coral made;
Those are pearls that were his eyes;
Nothing of him that doth fade,
But doth suffer a sea-change
Into something rich and strange.
Sea-nymphs hourly ring his knell:
Hark! Now I hear themding-dong bell.”
—William Shakespeare (15641616)