TY - JOUR

T1 - The Complementary Symmetric Functions

T2 - Connection Constants Using Negative Sets

AU - Damiani, E.

AU - D'Antona, O.

AU - Loeb, D. E.

PY - 1998/5/10

Y1 - 1998/5/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0007104620&partnerID=8YFLogxK

U2 - 10.1006/aima.1997.1698

DO - 10.1006/aima.1997.1698

M3 - Article

AN - SCOPUS:0007104620

SN - 0001-8708

VL - 135

SP - 207

EP - 219

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 2

ER -