Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Mock Alexander Polynomials(Australian National University, 2025) Güğümcü, Neslihan; Kauffman, L.H.; 01. Izmir Institute of Technology; 04. Faculty of Science; 04.02. Department of MathematicsIn this paper, we construct Mock Alexander polynomials for starred links and linkoids in surfaces. These polynomials are defined as state summations on link or linkoid diagrams that satisfy f = n, where f denotes the number of regions and n denotes the number of crossings of diagrams. These new invariants are chirality and reversibility sensitive. © The authors.Article Biquandle Power Brackets of Oriented Links(Tubitak Scientific & Technological Research Council Turkey, 2025) Güğümcü, Neslihan; Nelson, Sam; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyIn this paper, we introduce biquandle power brackets, an infinite family of invariants of oriented links containing the classical skein invariants and the quandle and biquandle 2-cocycle invariants as special cases. Biquandle power brackets are generalizations of biquandle brackets in which the values of Kauffman states also depend on the biquandle colors they admit. We provide example computations and discuss the relationship between these new invariants and the previous cases.