A generalization of carries process and Eulerian numbers

2013/06/12 by Fumihiko Nakano, Nakano, Fumihiko, Taizo Sadahiro +1
Mathematics · Physics and Astronomy · #05E99 #60C05 #60J10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1306.2790

openalex publication_date 2013/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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