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no. 3
An involution on RC-graphs and a conjecture on dual Schubert polynomials by Postnikov and Stanley
Gao, Yibo1
1 Massachusetts Institute of Technology Department of Mathematics Cambridge MA 02142, USA
Algebraic Combinatorics, Volume 3 (2020) no. 3, pp. 593-602

In this paper, we provide explicit formula for the dual Schubert polynomials of a special class of permutations using certain involution principals on RC-graphs, resolving a conjecture by Postnikov and Stanley.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.105
Classification: 05E05, 14N15
Keywords: Schubert polynomial, dual Schubert polynomial, Bruhat chains

Gao, Yibo 1

1 Massachusetts Institute of Technology Department of Mathematics Cambridge MA 02142, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Gao, Yibo. An involution on RC-graphs and a conjecture on dual Schubert polynomials by Postnikov and Stanley. Algebraic Combinatorics, Volume 3 (2020) no. 3, pp. 593-602. doi: 10.5802/alco.105

[1] Bergeron, Nantel; Billey, Sara C. RC-graphs and Schubert polynomials, Exp. Math., Volume 2 (1993) no. 4, pp. 257-269 | Zbl | MR | DOI

[2] Billey, Sara C.; Jockusch, William; Stanley, Richard P. Some combinatorial properties of Schubert polynomials, J. Algebr. Comb., Volume 2 (1993) no. 4, pp. 345-374 | Zbl | MR | DOI

[3] Fomin, Sergey; Kirillov, Anatol N. Yang–Baxter equation, symmetric functions and Grothendieck polynomials (1993) (arXiv preprint https://arxiv.org/abs/hep-th/9306005) | Zbl

[4] Fomin, Sergey; Stanley, Richard P. Schubert polynomials and the nil-Coxeter algebra, Adv. Math., Volume 103 (1994) no. 2, pp. 196-207 | Zbl | MR | DOI

[5] Gaetz, Christian; Gao, Yibo Padded Schubert polynomials and weighted enumeration of Bruhat chains (2019) (arXiv preprint https://arxiv.org/abs/1905.00047) | Zbl

[6] Gaetz, Christian; Gao, Yibo A combinatorial duality between the weak and strong Bruhat orders, J. Comb. Theory, Ser. A, Volume 171 (2020), pp. 105-178 | Zbl | MR | DOI

[7] Manivel, Laurent Symmetric functions, Schubert polynomials and degeneracy loci, SMF/AMS Texts and Monographs, 6, American Mathematical Society, Providence, RI; Société Mathématique de France, Paris, 2001, viii+167 pages (Translated from the 1998 French original by John R. Swallow, Cours Spécialisés [Specialized Courses], 3) | Zbl | MR

[8] Postnikov, Alexander; Stanley, Richard P. Chains in the Bruhat order, J. Algebr. Comb., Volume 29 (2009) no. 2, pp. 133-174 | Zbl | MR | DOI

[9] Stembridge, John R. A weighted enumeration of maximal chains in the Bruhat order, J. Algebr. Comb., Volume 15 (2002) no. 3, pp. 291-301 | Zbl | MR | DOI

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