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

2011/06/23 by Teresa Krick, Térésa Krick, Krick, Teresa +3
Computer Science · Engineering · Mathematics · #14Q10 #68W30 #Algebraic Geometry (math.AG) #Combinatorics #Commutative Algebra (math.AC) #Discrete mathematics #FOS: Mathematics #Mathematical analysis #Mathematics #Mathematics and Applications #Matrix polynomial #Monic polynomial #Polynomial #Polynomial and algebraic computation #Polynomial matrix #Sylvester matrix #graph theory and CDMA systems #math.AC #math.AG #msc:14Q10 #msc:68W30

paper · pdf · doi:10.48550/arxiv.1106.4770

12 pages, uses elsart.cls and yjsco.sty

arxiv created 2011/06/23 · openalex publication_date 2011/06/23 · arxiv updated 2011/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

In 1853, 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. More recently, 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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