ON A GRAPH CONNECTING HYPERBINARY EXPANSIONS

被引：0

作者：

Brunetti, Maurizio ^{[1
]}

D'Aniello, Alma ^{[1
]}

机构：

[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Naples, Italy

来源：

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD | 2019年 / 105卷 / 119期

关键词：

hyperbinary expansions; oriented graph; edge-coloured graph; WORDS;

D O I：

10.2298/PIM1919025B

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let n be any positive integer. 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 is an element of N such that the fundamental group of A(m) is Abelian.

引用

页码：25 / 38

页数：14

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