Claus Ernst, Van Pham
Abstract
In the paper, we introduce the concept of loop numbers of knot diagrams and we show that loop numbers are knot invariants for a large family of alternating knots. We also discuss relationships of loop numbers of knots with some classic knot invariants.
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In the paper, we introduce the concept of loop numbers of knot diagrams and we show that loop numbers are knot invariants for a large family of alternating knots. We also discuss relationships of loop numbers of knots with some classic knot invariants.
Key concepts: Knot (papermaking), Mathematics, Tricolorability, Skein relation, Knot invariant, Knot theory, Trefoil knot, Loop (graph theory)