A beautiful degree formula for Grothendieck polynomials was recently given by Pechenik, Speyer, and Weigandt (2021). We provide an alternative proof of their degree formula, utilizing the climbing chain model for Grothendieck polynomials introduced by Lenart, Robinson, and Sottile (2006). Moreover for any term order satisfying , we present the leading monomial of each homogeneous component of the Grothendieck polynomial , confirming a conjecture of Hafner (2022). We conclude with a conjecture for the leading monomial of each homogeneous component of in any term order satisfying .
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Keywords: Grothendieck polynomials, Rajchgot code, leading monomials
Dreyer, Matt 1; Meśzáros, Karola 1; St. Dizier, Avery 2
CC-BY 4.0
@article{ALCO_2024__7_3_627_0,
author = {Dreyer, Matt and Me\'sz\'aros, Karola and St.~Dizier, Avery},
title = {On the {Degree} of {Grothendieck} {Polynomials}},
journal = {Algebraic Combinatorics},
pages = {627--658},
publisher = {The Combinatorics Consortium},
volume = {7},
number = {3},
year = {2024},
doi = {10.5802/alco.358},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.358/}
}
TY - JOUR AU - Dreyer, Matt AU - Meśzáros, Karola AU - St. Dizier, Avery TI - On the Degree of Grothendieck Polynomials JO - Algebraic Combinatorics PY - 2024 SP - 627 EP - 658 VL - 7 IS - 3 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.358/ DO - 10.5802/alco.358 LA - en ID - ALCO_2024__7_3_627_0 ER -
%0 Journal Article %A Dreyer, Matt %A Meśzáros, Karola %A St. Dizier, Avery %T On the Degree of Grothendieck Polynomials %J Algebraic Combinatorics %D 2024 %P 627-658 %V 7 %N 3 %I The Combinatorics Consortium %U https://alco.centre-mersenne.org/articles/10.5802/alco.358/ %R 10.5802/alco.358 %G en %F ALCO_2024__7_3_627_0
Dreyer, Matt; Meśzáros, Karola; St. Dizier, Avery. On the Degree of Grothendieck Polynomials. Algebraic Combinatorics, Volume 7 (2024) no. 3, pp. 627-658. doi : 10.5802/alco.358. https://alco.centre-mersenne.org/articles/10.5802/alco.358/
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