2018/10/23 by Lang, Wolfdieter
#11Y55 #32H50 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1810.09787
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.