Combinatorics of continuants of continued fractions with 3 limits

We give combinatorial descriptions of the terms occurring in continuants of general continued fractions that diverge to three limits. Equating this combinatorics with the usual combinatorial description due to Euler induces nontrivial identities. Special cases and applications to counting sequences...

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Bibliographic Details
Published in:Journal of combinatorial theory. Series A 2022-02, Vol.186, p.105556, Article 105556
Main Authors: Bowman, Douglas, Schaumburg, Herman D.
Format: Article
Language:English
Subjects:
Continuants
Divergent continued fractions
Euler-Minding Theorem
Integer partitions
Linear recurrences
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Summary:We give combinatorial descriptions of the terms occurring in continuants of general continued fractions that diverge to three limits. Equating this combinatorics with the usual combinatorial description due to Euler induces nontrivial identities. Special cases and applications to counting sequences are given.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2021.105556