A generalization of the carries process

Takahiko Fujita, Fumihiko Nakano, Taizo Sadahiro

Research output: Contribution to journalConference articlepeer-review

1 Citation (Scopus)


We consider a carries process which is a generalization of that by Holte in the sense that (i) we take various digit sets, and (ii) we also consider negative base. Our results are: (i) eigenvalues and eigenvectors of the transition probability matrices, and their connection to combinatorics and representation theory, (ii) an application to the computation of the distribution of the sum of i.i.d. uniform r.v.'s on [0, 1], (iii) a relation to riffle shuffle.

Original languageEnglish
Pages (from-to)61-69
Number of pages9
JournalDiscrete Mathematics and Theoretical Computer Science
Publication statusPublished - 2014
Event26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 - Chicago, United States
Duration: 2014 Jun 292014 Jul 3


  • Carries process
  • Eulerian number
  • Riffle shuffle


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