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 -