A generalization of the carries process

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 rep...

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Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings vol. AT,...; no. Proceedings; pp. 61 - 70
Main Authors: Fujita, Takahiko, Nakano, Fumihiko, Sadahiro, Taizo
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 01.01.2014
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Series:DMTCS Proceedings
Subjects:
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[math.math-co] mathematics [math]/combinatorics [math.co]
carries process
Combinatorics
Computer Science
Discrete Mathematics
eulerian number
Mathematics
riffle shuffle
Eulerian number
Riffle shuffle
Carries process
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary: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.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2380