[Polytopes de Newton et polynômes symétriques de Grothendieck]
Les polynômes symétriques de Grothendieck sont des versions inhomogènes des polynômes de Schur qui apparaissent dans la K-théorie combinatoire. Un polynôme a un polytope de Newton saturé (SNP) si chaque point entier dans le polytope est un vecteur d'exposant. Nous montrons que les polytopes de Newton de ces polynômes de Grothendieck et leurs composants homogènes ont un SNP. En outre, le polytope de Newton de chaque composant homogène est un permutoèdre. Cela concerne les récentes conjectures de C. Monical–N. Tokcan–A. Yong et de A. Fink–K. Mészáros–A. St. Dizier dans ce cas spécial.
Symmetric Grothendieck polynomials are inhomogeneous versions of Schur polynomials that arise in combinatorial K-theory. A polynomial has saturated Newton polytope (SNP) if every lattice point in the polytope is an exponent vector. We show that the Newton polytopes of these Grothendieck polynomials and their homogeneous components have SNP. Moreover, the Newton polytope of each homogeneous component is a permutahedron. This addresses recent conjectures of C. Monical–N. Tokcan–A. Yong and of A. Fink–K. Mészáros–A. St. Dizier in this special case.
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@article{CRMATH_2017__355_8_831_0,
author = {Escobar, Laura and Yong, Alexander},
title = {Newton polytopes and symmetric {Grothendieck} polynomials},
journal = {Comptes Rendus. Math\'ematique},
pages = {831--834},
publisher = {Elsevier},
volume = {355},
number = {8},
year = {2017},
doi = {10.1016/j.crma.2017.07.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.07.003/}
}
TY - JOUR AU - Escobar, Laura AU - Yong, Alexander TI - Newton polytopes and symmetric Grothendieck polynomials JO - Comptes Rendus. Mathématique PY - 2017 SP - 831 EP - 834 VL - 355 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.07.003/ DO - 10.1016/j.crma.2017.07.003 LA - en ID - CRMATH_2017__355_8_831_0 ER -
%0 Journal Article %A Escobar, Laura %A Yong, Alexander %T Newton polytopes and symmetric Grothendieck polynomials %J Comptes Rendus. Mathématique %D 2017 %P 831-834 %V 355 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.07.003/ %R 10.1016/j.crma.2017.07.003 %G en %F CRMATH_2017__355_8_831_0
Escobar, Laura; Yong, Alexander. Newton polytopes and symmetric Grothendieck polynomials. Comptes Rendus. Mathématique, Tome 355 (2017) no. 8, pp. 831-834. doi : 10.1016/j.crma.2017.07.003. http://www.numdam.org/articles/10.1016/j.crma.2017.07.003/
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