The Tribonacci and ABC Representations of Numbers are Equivalent
Number Theory
2020-09-25 v2
Abstract
It is shown that the unique representation of positive integers in terms of tribonacci numbers and the unique representation in terms of iterated A, B and C sequences defined from the tribonacci word are equivalent. Two auxiliary representations are introduced to prove this bijection. It will be established directly on a node and edge labeled tribonacci tree as well as formally. A systematic study of the A, B and C sequences in terms of the tribonacci word is also presented.
Cite
@article{arxiv.1810.09787,
title = {The Tribonacci and ABC Representations of Numbers are Equivalent},
author = {Wolfdieter Lang},
journal= {arXiv preprint arXiv:1810.09787},
year = {2020}
}
Comments
23 pages, 3 figures and 3 tables This revised version takes care of comments, suggestions and questions of an unknown referee. The substitution rules have been changed. The old version is now obsolete