A generalization of carries process
| Project/Area Number |
26400149
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tsuda University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
ISHIKAWA Masao 岡山大学, 大学院自然科学研究科, 教授 (40243373)
FUJITA Takahiko 中央大学, 理工学部, 教授 (50144316)
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| Research Collaborator |
NAKANO Fumihiko 学習院大学, 理学部, 教授 (10291246)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 有限マルコフ連鎖 / 定常分布 / 混合時間 / 一般化置換群 / スペクトル / ランダムウォーク / 超平面配置 / 半群 / indexed permutation / primitive idempotents / eulerian number / 繰り上がり / オイラー数 / マルコフ連鎖 / decent |
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| Outline of Final Research Achievements |
When we add randomly generated integers, the sequence of the carries can be considered as a Markov chain. The transition probability matrix of this chain exhibits some remarkable properties, the eigenvalues and eigenvectors can be representd explicitly. We generalize this Markov chain and obtained an explicit formula which represents the eigenvalues and eigenvectors. We found a relation between this Markov chain and the riffle shuffle on the colored permutation groups.
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Report
(5 results)
Research Products
(2 results)
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[Presentation] A generalization of carries process2014
Author(s)
Takahiko Fujita, Fumihiko Nakano, and Taizo Sadahiro
Organizer
International conference on Formal Power Series and Algebraic Combinatorics
Place of Presentation
de Paul University
Year and Date
2014-06-29 – 2014-07-03
Related Report
