Schur Polynomials through Lindstr\"om Gessel Viennot Lemma
Combinatorics
2020-06-18 v2
Abstract
In this article, we use Lindstr\"om Gessel Viennot Lemma to give a short, combinatorial, visualizable proof of the identity of Schur polynomials -- the sum of monomials of Young tableaux equals to the quotient of determinants. As a by-product, we have a proof of Vandermonde determinant without words. We also prove the cauchy identity. In the remarks, we discuss factorial Schur polynomials, dual Cauchy identity and the relation beteen Newton interpolation formula.
Cite
@article{arxiv.2003.09215,
title = {Schur Polynomials through Lindstr\"om Gessel Viennot Lemma},
author = {Rui Xiong},
journal= {arXiv preprint arXiv:2003.09215},
year = {2020}
}