2015/03/13 by Toufik Mansour, Mansour, Toufik, Mark Shattuck +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Mathematical Dynamics and Fractals #math.CO #msc:05A30 #msc:11B37 #msc:11B75 #msc:11B83 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1503.03949
arxiv created 2015/03/13 · arxiv updated 2015/03/16
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.