# ALGEBRAIC COMBINATORICS

Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley
Algebraic Combinatorics, Volume 3 (2020) no. 2, pp. 301-307.

We study the action of a differential operator on Schubert polynomials. Using this action, we first give a short new proof of an identity of I. Macdonald (1991). We then prove a determinant conjecture of R. Stanley (2017). This conjecture implies the (strong) Sperner property for the weak order on the symmetric group, a property recently established by C. Gaetz and Y. Gao (2019).

Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/alco.93
Classification: 05E05,  06A07,  15A15,  05E10
Keywords: Sperner property, weak order, Schubert polynomial, Macdonald identity
@article{ALCO_2020__3_2_301_0,
author = {Hamaker, Zachary and Pechenik, Oliver and Speyer, David E and Weigandt, Anna},
title = {Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley},
journal = {Algebraic Combinatorics},
pages = {301--307},
publisher = {MathOA foundation},
volume = {3},
number = {2},
year = {2020},
doi = {10.5802/alco.93},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.93/}
}
Hamaker, Zachary; Pechenik, Oliver; Speyer, David E; Weigandt, Anna. Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley. Algebraic Combinatorics, Volume 3 (2020) no. 2, pp. 301-307. doi : 10.5802/alco.93. https://alco.centre-mersenne.org/articles/10.5802/alco.93/

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