Minimum lattice length of 2-bridge knots and links

초록

In nature, knots and links are found in diverse configurations. Studying various representations of knots and links is very important for navigating complexity of knots and links. One of the important invariants is the minimum lattice length which is the smallest number of sticks with unit length to represent a knot in the cubic lattice Z3. In this paper, we show that the minimum lattice length of 2-bridge knots or links with m integer tangles consisting of either all positive integer tangles or all negative integer tangles is bounded above by 6c(K) + 2m + 2h + 8, where c(K) is the minimum crossing number and his the number of tangles with a half twist. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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