Takahiko Fujita ; Fumihiko Nakano ; Taizo Sadahiro - A generalization of the carries process

dmtcs:2380 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) - https://doi.org/10.46298/dmtcs.2380
A generalization of the carries processArticle

Authors: Takahiko Fujita 1; Fumihiko Nakano 2; Taizo Sadahiro 3

  • 1 Faculty of Science and Engineering [Chuo]
  • 2 Department of Mathematics [Gakushuin]
  • 3 Department of Information Science [Tsuda]

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.

https://doi.org/10.46298/dmtcs.2380
Source: HAL:hal-01207591v1
Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Imported on: November 21, 2016
Keywords: Carries process,Eulerian number,Riffle shuffle,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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