✦ LIBER ✦

Heap-ordered Trees, 2-Partitions and Continued Fractions

✍ Scribed by Wen-Chin Chen; Wen-Chun Ni

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 139 KB
Volume: 15
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1994.1052

No coin nor oath required. For personal study only.

✦ Synopsis

This paper studies the enumerations and some interesting combinatorial properties of heap-ordered trees (HOTs). We first derive analytically the total numbers of (n)-node HOTs. We then show that there exists a 1-1 and onto correspondence between any two of the following four sets: the set of ((n+1))-node HOTs, the set of 2-partitions of (\mathbf{Z}{2 n}=) ({1,2, \ldots, 2 n}), the set of Young tableaux from (\mathbf{Z}{2 n}) without odd-length columns, and the set of weighted paths of length (2 n). These correspondences can not only be used to obtain the above enumeration quantities through combinatorial arguments, but can also relate their generating functions to continued fractions.

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