We prove that an inclusion-exclusion inspired expression of Schubert polynomials of permutations that avoid the patterns and 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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Classification: 05E05
Keywords: Schubert polynomial, principal specialization, nonnegative linear combination.
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@article{ALCO_2022__5_2_209_0, author = {M\'esz\'aros, Karola and Tanjaya, Arthur}, title = {Inclusion-exclusion on {Schubert} polynomials}, journal = {Algebraic Combinatorics}, pages = {209--226}, publisher = {The Combinatorics Consortium}, volume = {5}, number = {2}, year = {2022}, doi = {10.5802/alco.200}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.200/} }
TY - JOUR TI - Inclusion-exclusion on Schubert polynomials JO - Algebraic Combinatorics PY - 2022 DA - 2022/// SP - 209 EP - 226 VL - 5 IS - 2 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.200/ UR - https://doi.org/10.5802/alco.200 DO - 10.5802/alco.200 LA - en ID - ALCO_2022__5_2_209_0 ER -
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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