Alexandrov polinom - Kosmač, Juš (Matrika, 2018)
The main object of this article is to develop a way to distinguish among knots of different types. Some basic knowledge regarding presentations of groups and Tietze transformations is briefly recalled. A procedure of constructing the Wirtinger presentation of a knot group using the knot diagram is developed. Invariants of a knot type are defined with the use of derivation in a group ring - these are elementary ideals and knot polynomials. Their application is demonstrated in some examples.
Keywords: Alexander matrix; Alexander polynomial; Alexandrov polinom; Alexandrova matrika; elementarni ideal; elementary ideal; grupa vozla; knot group; knot polynomial; matematika; mathematics; vozelni polinom