Difference operators for partitions under the Littlewood decomposition

Dehaye, Paul-Olivier; Han, Guo-Niu; Xiong, Huan (2017). Difference operators for partitions under the Littlewood decomposition. The Ramanujan Journal, 44(1):197-225.

Abstract

The concept of $\mathit{t}$-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 $\mathit{t}$-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 $\mathit{t}$.

Abstract

The concept of $\mathit{t}$-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 $\mathit{t}$-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 $\mathit{t}$.

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Physical Sciences > Algebra and Number Theory English 2017 01 Feb 2017 07:47 26 Jan 2022 11:28 Springer 1382-4090 Green https://doi.org/10.1007/s11139-016-9807-z : FunderSNSF: Grant IDPP00P2_138906: Project TitleCombinatorics of partitions and number theoretic aspects

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