{rfName}
Pr

Indexed in

License and use

Citations

Altmetrics

Analysis of institutional authors

Manchón PmgAuthor
Share
Publications
>
Article

Pretzel knots up to nine crossings

Publicated to:Topology And Its Applications. 339 108583- - 2023-11-01 339(), DOI: 10.1016/j.topol.2023.108583

Authors: Díaz, R; Manchón, PMG

Affiliations

Univ Complutense Madrid, Fac Matemat, Dept Algebra Geometry & Topol, Madrid, Spain - Author
Univ Politecn Madrid, ETSIDI, Dept Appl Math Ind Engn, Madrid, Spain - Author
Universidad Complutense de Madrid - Author
Universidad Politécnica de Madrid - Author

Abstract

There are infinitely many pretzel links with the same Alexander polynomial (actually with trivial Alexander polynomial). By contrast, in this note we revisit the Jones polynomial of pretzel links and prove that, given a natural number S, there is only a finite number of pretzel links whose Jones polynomials have span S. More concretely, we provide an algorithm useful for deciding whether or not a given knot is pretzel. As an application we identify all the pretzel knots up to nine crossings, proving in particular that 812 is the first non-pretzel knot.

Keywords
jones polynomialkauffman bracketspanJones polynomialKauffman bracketPretzel linkSpan

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Topology And Its Applications, and although the journal is classified in the quartile Q3 (Agencia WoS (JCR)), its regional focus and specialization in Mathematics, give it significant recognition in a specific niche of scientific knowledge at an international level.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 1.25, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions May 2025)

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-05-18:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 3 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: Last Author (GONZALEZ MANCHON, PEDRO MARIA).