Polynomiality of shifted Plancherel averages and content evaluations
Annales mathématiques Blaise Pascal, Volume 24 (2017) no. 1, pp. 55-82.

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 $Q$-functions.

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 $Q$-fonctions de Schur factorielles.

Published online:
DOI: 10.5802/ambp.364
Classification: 05E05,  05A19,  60C05
Keywords: strict partition, Plancherel measure, Schur $Q$-function, content
Sho Matsumoto 1

1 Graduate School of Science and Engineering Kagoshima University 1-21-35, Korimoto Kagoshima-city, Kagoshima, Japan
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Sho Matsumoto. Polynomiality of shifted Plancherel averages and content evaluations. Annales mathématiques Blaise Pascal, Volume 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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