Polynomials Arising in Factoring Generalized Vandermonde Determinants Ii : A Condition for Monicity

In our previous paper [4] we observed that generalized Vandermonde determinants of the formwhere the are distinct points belonging to an interval [] of the real line, the index stands for the order, the sequence consists of ordered integers 0 ≤ < < … , can be factored as a product of the classical Vandermonde determinant and a On the other hand, we showed that when = the resulting polynomial in is a the Schur function which can be factored as a two-factors polynomial: the first is the constant times the monic polynomial while the second is a polynomial () of degree = − + 1. In this note we first present atypical application in which these factorizations arise and then we discuss a condition under which the polynomial () is