The Complementary Symmetric Functions: Connection Constants Using Negative Sets

Abstract

The coefficients relating the powers of x with sequences of the form[formula]are well known: in one sense, we have the elementary symmetric functions, and in the other, the complete symmetric functions. In this paper, through the use of the theory of negative sets, we give expansions of rational functions in terms of sequences of the above form extended as follows forn<0:pn(x)=(x-an)-1pn+1(x).As an application, we generalize many well-known combinatorial identities. © 1998 Academic Press.