Affiliation:
1. Dipartimento di Matematica e Applicazioni `R. Caccioppoli', Università di Napoli `Federico II', Napoli, Italy
Abstract
A hyperbinary expansion of n is a representation of n as sum of powers of
2, each power being used at most twice. 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. Such graph
suggests a method to measure the non-binarity of a hyperbinary expansion. We
discuss how it is related to (p,q)-hyperbinary expansions. Finally, we
identify those integers m\in\N such that the fundamental group of A(m)
is Abelian.
Publisher
National Library of Serbia