Inclusion-exclusion on Schubert polynomials
Algebraic Combinatorics, Volume 5 (2022) no. 2, pp. 209-226.

We prove that an inclusion-exclusion inspired expression of Schubert polynomials of permutations that avoid the patterns 1432 and 1423 is nonnegative. Our theorem implies a partial affirmative answer to a recent conjecture of Yibo Gao about principal specializations of Schubert polynomials. We propose a general framework for finding inclusion-exclusion inspired expression of Schubert polynomials of all permutations.

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Accepted:
Published online:
DOI: 10.5802/alco.200
Classification: 05E05
Keywords: Schubert polynomial, principal specialization, nonnegative linear combination.
Mészáros, Karola 1; Tanjaya, Arthur 2

1 Department of Mathematics Cornell University Ithaca, NY 14853 USA.
2 Department of Mathematics Cornell University Ithaca NY 14853 USA.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Mészáros, Karola; Tanjaya, Arthur. Inclusion-exclusion on Schubert polynomials. Algebraic Combinatorics, Volume 5 (2022) no. 2, pp. 209-226. doi : 10.5802/alco.200. https://alco.centre-mersenne.org/articles/10.5802/alco.200/

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