Generalized Stirling permutations, families of increasing trees and urn models
Generalized Stirling permutations, families of increasing trees and urn models
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DOI：
10.1016/j.jcta.2009.11.006
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发表时间：
2008-05
期刊：
影响因子：
--
通讯作者：
S. Janson;Markus Kuba;A. Panholzer
中科院分区：
文献类型：
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作者：
S. Janson;Markus Kuba;A. Panholzer
Bóna（2007）[6]研究了Gessel和Stanley（1978）[13]引入的斯特林排列类中上升、平稳和下降的分布。最近，Janson（2008）[17]证明了斯特林置换和平面递归树之间的联系，并证明了Bóna考虑的参数的联合正规律。在这里，我们将考虑广义斯特林置换，它扩展了Bóna（2007）[6]和Janson（2008）[17]的早期结果，并将它们与某些广义平面递归树族以及（k+1）元增树联系起来。我们还给出了两个不同的双射之间的某些家庭的增长树，这两个作为一个特殊情况的双射之间的三元增长树和平面递归树。为了描述感兴趣的参数的（渐近）行为，我们使用各种方法研究了三个（广义）Pólya urn模型。
Bóna (2007) [6] studied the distribution of ascents, plateaux and descents in the class of Stirling permutations, introduced by Gessel and Stanley (1978) [13]. Recently, Janson (2008) [17] showed the connection between Stirling permutations and plane recursive trees and proved a joint normal law for the parameters considered by Bóna. Here we will consider generalized Stirling permutations extending the earlier results of Bóna (2007) [6] and Janson (2008) [17], and relate them with certain families of generalized plane recursive trees, and also (k+1)-ary increasing trees. We also give two different bijections between certain families of increasing trees, which both give as a special case a bijection between ternary increasing trees and plane recursive trees. In order to describe the (asymptotic) behaviour of the parameters of interests, we study three (generalized) Pólya urn models using various methods.