A generalization of carries processes and Eulerian numbers

Fumihiko Nakano, Taizo Sadahiro

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)28-43
Number of pages16
JournalAdvances in Applied Mathematics
Issue number1
Publication statusPublished - 2014 Feb


  • Carries
  • Eulerian number
  • Markov chain


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