English

On a Graph Connecting Hyperbinary Expansions

Combinatorics 2016-10-05 v1

Abstract

Le n be any positive integer. A hyperbinary expansion of n is are presentation of n as sum of powers of 2, each power being used at most twice. In this paper we study some properties of a suitable edge-coloured and vertex-weighted oriented graph A(n) whose nodes are precisely the several hyperbinary representations of n. In particular, we identify those integers m in N such that the fundamental group of A(m) is abelian.

Keywords

Cite

@article{arxiv.1610.00903,
  title  = {On a Graph Connecting Hyperbinary Expansions},
  author = {M. Brunetti and A. D'Aniello},
  journal= {arXiv preprint arXiv:1610.00903},
  year   = {2016}
}
R2 v1 2026-06-22T16:09:50.582Z