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no. 2
Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley
Hamaker, Zachary1; Pechenik, Oliver2; Speyer, David E2; Weigandt, Anna2
1 Department of Mathematics University of Florida Gainesville, FL 32601, USA
2 Department of Mathematics University of Michigan Ann Arbor, MI 48109, USA
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).

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.93
Classification: 05E05, 06A07, 15A15, 05E10
Keywords: Sperner property, weak order, Schubert polynomial, Macdonald identity

Hamaker, Zachary 1; Pechenik, Oliver 2; Speyer, David E 2; Weigandt, Anna 2

1 Department of Mathematics University of Florida Gainesville, FL 32601, USA
2 Department of Mathematics University of Michigan Ann Arbor, MI 48109, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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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