Schubert polynomials, 132-patterns, and Stanley’s conjecture
Weigandt, Anna E.1
1 University of Illinois at Urbana-Champaign Dept. of Mathematics 1409 W. Green St. Urbana IL 61801, USA
Algebraic Combinatorics, Tome 1 (2018) no. 4, pp. 415-423.

Motivated by a recent conjecture of R. P. Stanley we offer a lower bound for the sum of the coefficients of a Schubert polynomial in terms of 132-pattern containment.

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DOI : 10.5802/alco.27
Mots-clés : Schubert polynomials, permutation patterns
Weigandt, Anna E. 1

1 University of Illinois at Urbana-Champaign Dept. of Mathematics 1409 W. Green St. Urbana IL 61801, USA 
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Weigandt, Anna E. Schubert polynomials, 132-patterns, and Stanley’s conjecture. Algebraic Combinatorics, Tome 1 (2018) no. 4, pp. 415-423. doi : 10.5802/alco.27. http://archive.numdam.org/articles/10.5802/alco.27/

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

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

[3] Fomin, Sergey; Kirillov, Anatol N. The Yang-Baxter equation, symmetric functions, and Schubert polynomials, Discrete Math., Volume 153 (1996) no. 1-3, pp. 123-143 | DOI | MR | Zbl

[4] Knutson, Allen; Miller, Ezra Gröbner geometry of Schubert polynomials, Ann. Math. (2005), pp. 1245-1318 | DOI | Zbl

[5] Lascoux, Alain; Schützenberger, Marcel-Paul Polynômes de Schubert, C. R. Math. Acad. Sci. Paris, Volume 295 (1982) no. 3, pp. 447-450 | Zbl

[6] Macdonald, Ian G. Notes on Schubert polynomials, Publications du Laboratoire de combinatoire et d’informatique mathématique, 6, Université du Québec à Montréal, 1991

[7] Manivel, Laurent Symmetric functions, Schubert polynomials, and degeneracy loci, SMF/AMS Texts and Monographs, 6, American Mathematical Society, 2001 | MR | Zbl

[8] Stanley, Richard P. Some Schubert shenanigans (2017) (https://arxiv.org/abs/1704.00851)

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