A generalization of carries processes and Eulerian numbers

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Feb 2014Embargo end date: 01 Jun 2013 English Publisher:Elsevier BVJournal:Advances in Applied Mathematics, volume 53, pages 28-43 (issn: 0196-8858,

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Authors: Fumihiko Nakano; Taizo Sadahiro;

doi: 10.1016/j.aam.2013.09.005 , 10.48550/arxiv.1306.2790

arXiv: 1306.2790

A generalization of carries processes and Eulerian numbers

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Abstract

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.

16 pages, 2 figures

Related Organizations

Gakushuin University
Japan
Tsuda University
Japan

Keywords

60C05, 60J10, 05E99, Combinatorial probability, Markov chain, Probability (math.PR), Eulerian number, carries, Markov chains (discrete-time Markov processes on discrete state spaces), Algebraic combinatorics, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Mathematics - Probability

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