کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4650184 | 1342478 | 2007 | 14 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Some set partition statistics in non-crossing partitions and generating functions Some set partition statistics in non-crossing partitions and generating functions](/preview/png/4650184.png)
In this paper we shall give the generating functions for the enumeration of non-crossing partitions according to some set partition statistics explicitly, which are based on whether a block is singleton or not and is inner or outer. Using weighted Motzkin paths, we find the continued fraction form of the generating functions. There are bijections between non-crossing partitions, Dyck paths and non-nesting partitions, hence we can find applications in the enumeration of Dyck paths and non-nesting partitions. We shall also study the integral representation of the enumerating polynomials for our statistics. As an application of integral representation, we shall give some remarks on the enumeration of inner singletons in non-crossing partitions, which is equivalent to one of udu's at high level in Dyck paths investigated in [Y. Sun, The statistic “number of udu's” in Dyck paths, Discrete Math. 284 (2004) 177–186].
Journal: Discrete Mathematics - Volume 307, Issue 24, 28 November 2007, Pages 3147–3160