Heap-ordered trees, 2-Partitions, and Continued Fractions
Journal
European Journal of Combinatorics
Journal Volume
15
Journal Issue
6
Pages
513-517
Date Issued
1994
Date
1994
Author(s)
Ni, Wen-Chun
Abstract
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 Z2n = {1, 2,…, 2n} the set of Young tableaux from Z2n without odd-length columns, and set of weighted paths of length 2n. These correspondence can not only be used to obtain the above enumeration quantities through combinatorial arguments, but can also relate their generating functions to continued fractions. © 1994 Academic Press. All rights reserved.
Type
journal article
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