A generalization of carries process and Eulerian numbers
Probability
2013-09-24 v2 Combinatorics
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.
Cite
@article{arxiv.1306.2790,
title = {A generalization of carries process and Eulerian numbers},
author = {Fumihiko Nakano and Taizo Sadahiro},
journal= {arXiv preprint arXiv:1306.2790},
year = {2013}
}
Comments
16 pages, 2 figures