Construction of some special subsequences within a Farey sequence
Mathematical Physics
2007-05-23 v1 High Energy Physics - Theory
math.MP
Number Theory
Exactly Solvable and Integrable Systems
Abstract
Recently it has been found that some special subsequences within a Farey sequence play a crucial role in determining the ranges of coupling constant for which quantum soliton states can exist for an integrable derivative nonlinear Schrodinger model. In this article, we find a novel mapping which connects two such subsequences belonging to Farey sequences of different orders. By using this mapping, we construct an algorithm to generate all of these special subsequences within a Farey sequence. We also derive the continued fraction expansions for all the elements belonging to a subsequence and observe a close connection amongst the corresponding expansion coefficients.
Cite
@article{arxiv.math-ph/0312021,
title = {Construction of some special subsequences within a Farey sequence},
author = {B. Basu-Mallick and Tanaya Bhattacharyya and Diptiman Sen},
journal= {arXiv preprint arXiv:math-ph/0312021},
year = {2007}
}
Comments
latex, 8 pages