Schubert polynomials form a basis of the polynomial ring $\mathbb{Q}[x_1, x_2, \dots ]$. This basis and its structure constants have received extensive study. Recently, Pan and Yu initiated the study of top Lascoux polynomials. These polynomials form a basis of the vector space $\widehat{V}$, a sub-algebra of $\mathbb{Q}[x_1, x_2, \dots ]$ where each graded piece has finite dimension. This paper connects Schubert polynomials and top Lascoux polynomials via a simple operator. We use this connection to show these two bases share the same structure constants. We also translate several results on Schubert polynomials to top Lascoux polynomials, including combinatorial formulas for their monomial expansions and supports.
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Keywords: Schubert polynomials, Lascoux polynomials, Key polynomials
Yu, Tianyi 1
CC-BY 4.0
@article{ALCO_2025__8_4_955_0,
author = {Yu, Tianyi},
title = {Connection between {Schubert} polynomials and top {Lascoux} polynomials},
journal = {Algebraic Combinatorics},
pages = {955--970},
publisher = {The Combinatorics Consortium},
volume = {8},
number = {4},
year = {2025},
doi = {10.5802/alco.439},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.439/}
}
TY - JOUR AU - Yu, Tianyi TI - Connection between Schubert polynomials and top Lascoux polynomials JO - Algebraic Combinatorics PY - 2025 SP - 955 EP - 970 VL - 8 IS - 4 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.439/ DO - 10.5802/alco.439 LA - en ID - ALCO_2025__8_4_955_0 ER -
%0 Journal Article %A Yu, Tianyi %T Connection between Schubert polynomials and top Lascoux polynomials %J Algebraic Combinatorics %D 2025 %P 955-970 %V 8 %N 4 %I The Combinatorics Consortium %U https://alco.centre-mersenne.org/articles/10.5802/alco.439/ %R 10.5802/alco.439 %G en %F ALCO_2025__8_4_955_0
Yu, Tianyi. Connection between Schubert polynomials and top Lascoux polynomials. Algebraic Combinatorics, Volume 8 (2025) no. 4, pp. 955-970. doi : 10.5802/alco.439. https://alco.centre-mersenne.org/articles/10.5802/alco.439/
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