Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

Browse

Filters

2021 - 20233

Settings

Has files: YesSubject: search.filters.subject.Knotoids

Search Results

Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 7
    Citation - Scopus: 8
    Invariants of Multi-Linkoids
    (Springer Basel Ag, 2023) Gabrovsek, Bostjan; Güğümcü, Neslihan
    In this paper, we extend the definition of a knotoid to multilinkoids that consist of a finite number of knot and knotoid components. We study invariants of multi-linkoids, such as the Kauffman bracket polynomial, ordered bracket polynomial, the Kauffman skein module, and the T-invariant in relation with generalized T-graphs.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 8
    Invariants of Bonded Knotoids and Applications To Protein Folding
    (MDPI, 2022) Güğümcü, Neslihan; Gabrovsek, Bostjan; Kauffman, Louis H.
    In this paper, we study knotoids with extra graphical structure (bonded knotoids) in the settings of rigid vertex and topological vertex graphs. We construct bonded knotoid invariants by applying tangle insertion and unplugging at bonding sites of a bonded knotoid. We demonstrate that our invariants can be used for the analysis of the topological structure of proteins.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Quantum Invariants of Knotoids
    (Springer, 2021) Güğümcü, Neslihan; Kauffman, Louis H.
    In this paper, we construct quantum invariants for knotoid diagrams in R-2. The diagrams are arranged with respect to a given direction in the plane (Morse knotoids). A Morse knotoid diagram can be decomposed into basic elementary diagrams each of which is associated to a matrix that yields solutions of the quantum Yang-Baxter equation. We recover the bracket polynomial, and define the rotational bracket polynomial, the binary bracket polynomial, the Alexander polynomial, the generalized Alexander polynomial and an infinity of specializations of the Homflypt polynomial for Morse knotoids via quantum state sum models.