Double Schubert polynomials do have saturated Newton polytopes
Forum of Mathematics, Sigma, Tome 11 (2023)
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We prove that double Schubert polynomials have the saturated Newton polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory of multidegrees. We introduce a notion of standardization of ideals that enables us to study nonstandard multigradings. This allows us to show that the support of the multidegree polynomial of each Cohen–Macaulay prime ideal in a nonstandard multigrading, and in particular, that of each Schubert determinantal ideal is a discrete polymatroid.
@article{10_1017_fms_2023_101,
author = {Federico Castillo and Yairon Cid-Ruiz and Fatemeh Mohammadi and Jonathan Monta\~no},
title = {Double {Schubert} polynomials do have saturated {Newton} polytopes},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {11},
year = {2023},
doi = {10.1017/fms.2023.101},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.101/}
}
TY - JOUR AU - Federico Castillo AU - Yairon Cid-Ruiz AU - Fatemeh Mohammadi AU - Jonathan Montaño TI - Double Schubert polynomials do have saturated Newton polytopes JO - Forum of Mathematics, Sigma PY - 2023 VL - 11 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.101/ DO - 10.1017/fms.2023.101 LA - en ID - 10_1017_fms_2023_101 ER -
%0 Journal Article %A Federico Castillo %A Yairon Cid-Ruiz %A Fatemeh Mohammadi %A Jonathan Montaño %T Double Schubert polynomials do have saturated Newton polytopes %J Forum of Mathematics, Sigma %D 2023 %V 11 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.101/ %R 10.1017/fms.2023.101 %G en %F 10_1017_fms_2023_101
Federico Castillo; Yairon Cid-Ruiz; Fatemeh Mohammadi; Jonathan Montaño. Double Schubert polynomials do have saturated Newton polytopes. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.101
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