Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4624787 | Advances in Applied Mathematics | 2014 | 16 Pages |
Abstract
We study a generalization of Holteʼs 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Fumihiko Nakano, Taizo Sadahiro,