Determinantal Formulas for SEM Expansions of Schubert Polynomials
Combinatorics
2021-04-13 v1
Abstract
We show that for any permutation that avoids a certain set of 13 patterns of lengths 5 and 6, the Schubert polynomial can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi-Trudi identity. For such , this determinantal formula is equivalent to a (signed) subtraction-free expansion of in the basis of standard elementary monomials.
Keywords
Cite
@article{arxiv.2104.04612,
title = {Determinantal Formulas for SEM Expansions of Schubert Polynomials},
author = {Hassan Hatam and Joseph Johnson and Ricky Ini Liu and Maria Macaulay},
journal= {arXiv preprint arXiv:2104.04612},
year = {2021}
}