Construction of some special subsequences within a Farey sequence
B. Basu-Mallick, Tanaya Bhattacharyya, Diptiman Sen

TL;DR
This paper introduces a new mapping and algorithm to generate special subsequences within Farey sequences, revealing their structure and continued fraction properties, which are relevant for quantum soliton state analysis.
Contribution
It presents a novel mapping between subsequences of different Farey sequence orders and an algorithm to generate these subsequences, along with their continued fraction expansions.
Findings
Established a new connection between Farey subsequences of different orders
Developed an algorithm to generate all special subsequences within a Farey sequence
Derived continued fraction expansions for elements of these subsequences
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.
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Taxonomy
TopicsNonlinear Waves and Solitons · Optical Network Technologies · Algebraic structures and combinatorial models
