A generalization of carries processes and Eulerian numbers

作者：Nakano Fumihiko; Sadahiro Taizo^*

来源：Advances in Applied Mathematics, 2014, 53: 28-43.

DOI：10.1016/j.aam.2013.09.005

• Carries
• Markov chain
• Eulerian number

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.

• 出版日期2014-2