Generalized q-Calkin-Wilf trees and c-hyper m-expansions of integers
Combinatorics
2015-03-16 v1
Abstract
A hyperbinary expansion of a positive integer n is a partition of n into powers of 2 in which each part appears at most twice. In this paper, we consider a generalization of this concept and a certain statistic on the corresponding set of expansions of n. We then define q-generalized m-ary trees whose vertices are labeled by ratios of two consecutive terms within the sequence of distribution polynomials for the aforementioned statistic. When m = 2, we obtain a variant of a previously considered q-Calkin-Wilf tree.
Keywords
Cite
@article{arxiv.1503.03949,
title = {Generalized q-Calkin-Wilf trees and c-hyper m-expansions of integers},
author = {Toufik Mansour and Mark Shattuck},
journal= {arXiv preprint arXiv:1503.03949},
year = {2015}
}