ABSTRACT
Let be distinct positive real numbers and m be any integer. Every symmetric polynomial induces a symmetric matrix We obtain the determinants of such matrices with an aim to find the determinants of and for (where is the set of natural numbers) in terms of the Schur polynomials. We also discuss and compute determinant of the matrix for any integer m in terms of the Schur and skew-Schur polynomials.
2010 Mathematics Subject Classifications:
Acknowledgments
The authors are grateful to a referee for valuable comments. Thanks are also due to an editor who helped us in improving the exposition of the final version.
Disclosure statement
No potential conflict of interest was reported by the authors.