Morphic Words and Nested Recurrence Relations
Combinatorics
2013-07-02 v1
Abstract
We explore a family of nested recurrence relations with arbitrary levels of nesting, which have an interpretation in terms of fixed points of morphisms over a countably infinite alphabet. Recurrences in this family are related to a number of well-known sequences, including Hofstadter's G sequence and the Conolly and Tanny sequences. For a recurrence a(n) in this family with only finitely terms, we provide necessary and sufficient conditions for the limit a(n)/n to exist.
Cite
@article{arxiv.1307.0153,
title = {Morphic Words and Nested Recurrence Relations},
author = {Marcel Celaya and Frank Ruskey},
journal= {arXiv preprint arXiv:1307.0153},
year = {2013}
}
Comments
20 pages