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Cubic harmonics and Bernoulli numbers
| Title: | Cubic harmonics and Bernoulli numbers |
| Authors: | Iwasaki, Katsunori Browse this author →KAKEN DB |
| Keywords: | Polyhedral harmonics | | Cube | | Reflection groups | | Invariant theory | | Invariant differential equations | | Generating functions | | Partitions | | Young diagrams | | Bernoulli numbers |
| Issue Date: | Aug-2012 |
| Publisher: | Elsevier |
| Journal Title: | Journal of Combinatorial Theory, Series A |
| Volume: | 119 |
| Issue: | 6 |
| Start Page: | 1216 |
| End Page: | 1234 |
| Publisher DOI: | 10.1016/j.jcta.2012.02.010 |
| Abstract: | 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. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/49687 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 岩崎 克則
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