English

Determinantal Formulas for SEM Expansions of Schubert Polynomials

Combinatorics 2021-04-13 v1

Abstract

We show that for any permutation ww that avoids a certain set of 13 patterns of lengths 5 and 6, the Schubert polynomial Sw\mathfrak S_w can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi-Trudi identity. For such ww, this determinantal formula is equivalent to a (signed) subtraction-free expansion of Sw\mathfrak S_w 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}
}