A partial order on partitions and the generalized Vandermonde determinant
نویسنده
چکیده
We introduce a partial order on partitions which permits an inductive proof on partitions. As an example of this technique, we reprove the discriminant formula for the generalized Vandermonde determinant. 2003 Elsevier Inc. All rights reserved.
منابع مشابه
A Generalized Vandermonde Determinant
Interpolation theory suggests a generalization of the usual Vandermonde determinant to numbers with multiplicities. We prove a discriminant formula for this generalized Vandermonde determinant and give an application to the Hermite interpolation problem.
متن کاملOn the Irreducibility of Generalized Vandermonde Determinants
We find geometric and arithmetic conditions on a finite set of integer exponents and the characteristic of a field k in order to characterize the irreducibility of the determinant of the generic Vandermonde matrix determined by these exponents in the algebraic closure of k. Tools from Tropical Geometry are then applied in order to characterize those determinants that are irreducible over any fi...
متن کاملTropicalization and Irreducibility of Generalized Vandermonde Determinants
We find geometric and arithmetic conditions in order to characterize the irreducibility of the determinant of the generic Vandermonde matrix over the algebraic closure of any field k. We also characterize those determinants whose tropicalization with respect to the variables of a row is irreducible.
متن کاملA Numerical Method for Solving Time-Invariant System by Generalized Inverse Vandermonde Matrix
A simple numerical algorithm based on the generalized Inverse Vandermore matrix for evaluation of time response to a time-invariant system is proposed. The system is assumed to be governed by a high order linear differential equation with constant coefficients. The technique involves determination of the partial-fraction expansion of rational functions. Only synthetic division and longhand divi...
متن کاملPolynomials arising in factoring generalized Vandermonde determinants II: A condition for monicity
h our previous paper [l], we observed that generalized Vandermonde determinants of the form vn;~(ll,. , G) = \q” / I 1 5 i, k 5 n, 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 Schu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004