La mesure de Plancherel décalée est une mesure de probabilité naturelle sur les partitions strictes. Nous démontrons une propriété de polynomialité pour les moyennes de mesures de Plancherel décalées. Comme application, nous donnons une nouvelle preuve de certaines formules d’évaluation des contenus obtenues par Han et Xiong très récemment. Nous utilisons, comme outil principal, les -fonctions de Schur factorielles.
The shifted Plancherel measure is a natural probability measure on strict partitions. We prove a polynomiality property for the averages of the shifted Plancherel measure. As an application, we give alternative proofs of some content evaluation formulas, obtained by Han and Xiong very recently. Our main tool is factorial Schur -functions.
Keywords: strict partition, Plancherel measure, Schur $Q$-function, content
Mots clés : partitions strictes, mesure de Plancherel, $Q$-fonction de Schur, contenu
Sho Matsumoto 1
CC-BY 4.0
@article{AMBP_2017__24_1_55_0,
author = {Sho Matsumoto},
title = {Polynomiality of shifted {Plancherel} averages and content evaluations},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {55--82},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {24},
number = {1},
year = {2017},
doi = {10.5802/ambp.364},
language = {en},
url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.364/}
}
TY - JOUR AU - Sho Matsumoto TI - Polynomiality of shifted Plancherel averages and content evaluations JO - Annales mathématiques Blaise Pascal PY - 2017 SP - 55 EP - 82 VL - 24 IS - 1 PB - Annales mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.364/ DO - 10.5802/ambp.364 LA - en ID - AMBP_2017__24_1_55_0 ER -
%0 Journal Article %A Sho Matsumoto %T Polynomiality of shifted Plancherel averages and content evaluations %J Annales mathématiques Blaise Pascal %D 2017 %P 55-82 %V 24 %N 1 %I Annales mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.364/ %R 10.5802/ambp.364 %G en %F AMBP_2017__24_1_55_0
Sho Matsumoto. Polynomiality of shifted Plancherel averages and content evaluations. Annales mathématiques Blaise Pascal, Tome 24 (2017) no. 1, pp. 55-82. doi : 10.5802/ambp.364. https://ambp.centre-mersenne.org/articles/10.5802/ambp.364/
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