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Schubert polynomials and patterns in permutations
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DOI：10.1007/s00209-026-04049-w.png)
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Abstract
En 中文
This paper investigates the size of the support of a Schubert polynomial delta(w)(x) indexed by a permutation omega. This number also equals the number of lattice points in the Newton polytope of delta(w)(x). We establish a lower bound for this number in terms of the occurrences of patterns in w. The analysis is carried out in the general framework of dual characters of flagged Weyl modules. Our result considerably improves the bounds for principal specializations of Schubert polynomials or dual flagged Weyl characters previously obtained by Weigandt, Gao, and M & eacute;sz & aacute;ros-St. Dizier-Tanjaya. Some problems and conjectures are discussed.
Keywords:
Schubert polynomial
Key polynomial
Flagged Weyl module
Dual character
Support
Principal specialization