Polynomials arising in factoring generalized Vandermonde determinants II: A condition for monicity

✍ Scribed by S. De Marchi

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 362 KB
• Volume: 15
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(02)80016-7

✦ Synopsis

our previous paper [l], we observed that generalized Vandermonde determinants of the form vn;~(ll,.

, G) = \q" / I

where the 2, are distinct points belonging to an interval [a, b] of the real line, the index n stands for the order, the sequence p consists of ordered integers 0 5 pi < ~2 < ... < pLn, can be factored as a product of the classical Vandermonde determinant and a Schur functzon. On the other hand, we showed that when I = x,, the resulting polynomial in x is a Schur function which can be factored as a two-factors polynomial: the first is the constant nyzi zi' times the manic polynomial ~,"=;'(z-z~), while the second is a polynomial PAT(I) of degree A4 = m,_r -n + 1. In this paper, we first present a typical application in which these factorizations arise and then we discuss a condition under which the polynomial PAI is monk.