A generalization of carries processes and Eulerian numbers
A generalization of carries processes and Eulerian numbers
复制标题
进位过程和欧拉数的推广
DOI：
10.1016/j.aam.2013.09.005
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
T
中科院分区：
文献类型：
--
作者：
Nakano;F.;Sadahiro;T
研究了非标准计数系统中“进位”的马尔可夫链的转移概率矩阵——Holte奇异矩阵的推广。平稳分布被明确地描述为欧拉数和麦克马洪数的推广。我们还证明了类似的性质，甚至对具有负基数的记数系统也成立。
We study a generalization of Holteʼs amazing matrix, the transition probability matrix of the Markov chains of the ‘carries’ in anon-standardnumeration 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.