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Article

Extreme coefficients of Jones polynomials and graph theory

Publicated to:Journal Of Knot Theory And Its Ramifications. 13 (2): 277-295 - 2004-03-01 13(2), DOI: 10.1142/S0218216504003135

Authors: Manchon, PMG;

Affiliations

Abstract

We find families of prime diagrams of knots with arbitrary extreme coefficients in their Jones polynomials. Some graph theory is presented in connection with this problem, generalizing ideas by Yongju Bae and Morton [4] and giving a positive answer to a question in their paper.

Keywords

Algebra and number theoryGeometry and topologyInterdisciplinarMatemática / probabilidade e estatísticaMathematics

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Journal Of Knot Theory And Its Ramifications due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2004, it was in position , thus managing to position itself as a Q2 (Segundo Cuartil), in the category Algebra and Number Theory. Notably, the journal is positioned en el Cuartil Q3 for the agency WoS (JCR) in the category Mathematics.

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: 2.36, 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 Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-07, the following number of citations:

  • WoS: 11
  • Scopus: 12
  • Open Alex: 13

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 2025-06-07:

  • 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: 7 (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: First Author (Manchon, PMG) .

the author responsible for correspondence tasks has been Manchon, PMG.