A generalization of carries processes and Eulerian numbers |
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Institution: | 1. Department of Mathematics, Gakushuin University, 1-5-1, Mejiro, Toshima-ku, Tokyo, 171-8588, Japan;2. Department of Computer Science, Tsuda College, Tokyo, Japan |
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Abstract: | We study a generalization of Holte?s amazing matrix, the transition probability matrix of the Markov chains of the ‘carries’ in a non-standard numeration system. The stationary distributions are explicitly described by the numbers which can be regarded as a generalization of the Eulerian numbers and the MacMahon numbers. We also show that similar properties hold even for the numeration systems with the negative bases. |
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Keywords: | Carries Markov chain Eulerian number |
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