Abstract

TORO, MARGARITA  and  RODRIGUEZ, JOSÉ GREGORIO. Triplets associated to virtual knot diagrams. Integración - UIS [online]. 2011, vol.29, n.2, pp.97-108. ISSN 0120-419X.

Abstract. In this paper we study the set T of triplets (E,A,B), where E ∈ {-1, 1}ⁿ, A ∈ ℤⁿ and B is an integral antisymmetric matrix of order n, n ∈ ℕ∪{0}. We define an equivalence relation on the set T and then we study properties of its equivalence classes. We describe a method to assign to each virtual knot diagram a triplet, and this is the motivation to study the set of triplets. As the assignation of a triplet depends on the virtual knot diagram, it is not a virtual knot invariant. But we try to solve this problem by using the equivalence relation defined on T.

Keywords : : triplets; virtual knots diagrams; virtual knots; based matrix; nudal codes; combinatorial knots.

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