We give necessary conditions for the positivity of Littlewood–Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if appears as a summand in the decomposition into irreducibles of , then ’s diagram is contained in ’s diagram.
Nous donnons des conditions nécessaires de positivité pour les coefficients de Littlewood–Richardson et pour les coefficients SXP. Nous en déduisons la condition nécessaire de positivité suivante pour les coefficients du pléthysme : si apparaît dans la décomposition en irréductibles de , alors le diagramme de est contenu dans celui de .
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Álvaro Gutiérrez 1; Mercedes H. Rosas 1
@article{CRMATH_2023__361_G7_1163_0, author = {\'Alvaro Guti\'errez and Mercedes H. Rosas}, title = {Necessary conditions for the positivity of {Littlewood{\textendash}Richardson} and plethystic coefficients}, journal = {Comptes Rendus. Math\'ematique}, pages = {1163--1173}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.468}, language = {en}, }
TY - JOUR AU - Álvaro Gutiérrez AU - Mercedes H. Rosas TI - Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients JO - Comptes Rendus. Mathématique PY - 2023 SP - 1163 EP - 1173 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.468 LA - en ID - CRMATH_2023__361_G7_1163_0 ER -
%0 Journal Article %A Álvaro Gutiérrez %A Mercedes H. Rosas %T Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients %J Comptes Rendus. Mathématique %D 2023 %P 1163-1173 %V 361 %I Académie des sciences, Paris %R 10.5802/crmath.468 %G en %F CRMATH_2023__361_G7_1163_0
Álvaro Gutiérrez; Mercedes H. Rosas. Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1163-1173. doi : 10.5802/crmath.468. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.468/
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