Construction of some special subsequences within a Farey sequence

Details Construction of some special subsequences within a Farey sequence Construction of some special subsequences within a Farey sequence

2003-12-09

arxiv.org/abs/math-ph/0312021v1

Physics

Mathematical Physics

latex, 8 pages

Scientific paper

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.

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