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arXiv · 1511.02804

Difference operators for partitions under the Littlewood decomposition

Paul-Olivier Dehaye·Guo-Niu Han·Huan Xiong
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Abstract

The concept of $t$-difference operator for functions of partitions is introduced to prove a generalization of Stanley's theorem on polynomiality of Plancherel averages of symmetric functions related to contents and hook lengths. Our extension uses a generalization of the notion of Plancherel measure, based on walks in the Young lattice with steps given by the addition of $t$-hooks. It is well-known that the hook lengths of multiples of $t$ can be characterized by the Littlewood decomposition. Our study gives some further information on the contents and hook lengths of other congruence classes modulo $t$.

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Paul-Olivier Dehaye, Guo-Niu Han, Huan Xiong. 2015-11-09. Difference operators for partitions under the Littlewood decomposition. https://arxiv.org/abs/1511.02804

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