On Vandermonde determinants via $n$-determinants
Combinatorics
2022-02-07 v1 Number Theory
Abstract
We use earlier defined notion of - determinant to investigate sub-determinants of an extended Vandermonde matrix. Firstly, we demonstrate our method on a number of particular cases. Then we prove that all these results may be stated in terms of Schur's polynomials. In our main result, we prove that Schur polynomials are equal to minors of a fixed matrix, which entries are formed of elementary symmetric polynomials. Such a formula is known as the second Jaccobi-Trudi identity.
Keywords
Cite
@article{arxiv.2202.02075,
title = {On Vandermonde determinants via $n$-determinants},
author = {Milan Janjic},
journal= {arXiv preprint arXiv:2202.02075},
year = {2022}
}