Cubic harmonics and Bernoulli numbers

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:119

Article

Iwasaki, Katsunori

关键词: Polyhedral harmonics;    Cube;    Reflection groups;    Invariant theory;    Invariant differential equations;    Generating functions;    Partitions;    Young diagrams;    Bernoulli numbers;   

DOI  :  10.1016/j.jcta.2012.02.010

来源: Elsevier

【 摘 要 】

The functions satisfying the mean value property for an n-dimensional cube are determined explicitly. This problem is related to invariant theory for a finite reflection group, especially to a system of invariant differential equations. Solving this problem is reduced to showing that a certain set of invariant polynomials forms an invariant basis. After establishing a certain summation formula over Young diagrams, the latter problem is settled by considering a recursion formula involving Bernoulli numbers. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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