Sylvester's double sums: an inductive proof of the general case

Details Sylvester's double sums: an inductive proof of the general case Sylvester's double sums: an inductive proof of the general case

2011-06-23

arxiv.org/abs/1106.4770v1

Mathematics

Commutative Algebra

12 pages, uses elsart.cls and yjsco.sty

Scientific paper

In 1853 J. Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these sets. In 2009, in a joint work with C. D'Andrea and H. Hong we gave the complete description of all the members of the family as expressions in the coefficients of these polynomials. In 2010, M.-F. Roy and A. Szpirglas presented a new and natural inductive proof for the cases considered by Sylvester. Here we show how induction also allows to obtain the full description of Sylvester's double-sums.

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