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math.GT2025
Multiple points of view: The simultaneous crossing number for knots with doubly transvergent diagrams
Christoph Lamm, Michael Eisermann
The simultaneous crossing number is a new knot invariant which is defined for strongly invertible knots having diagrams with two orthogonal transvergent axes of strong inversions.…
math.GT2024
The enumeration of doubly symmetric diagrams for strongly positive amphicheiral knots
Christoph Lamm
This is the second part of the article on doubly symmetric diagrams and strongly positive amphicheiral knots. We develop an enumeration strategy for prime knots given by doubly sym…
math.GT2023
Strongly positive amphicheiral knots with doubly symmetric diagrams
Christoph Lamm
We determine the prime strongly positive amphicheiral knots up to 16 crossings and show that a large fraction of them admit knot diagrams with a double symmetry (rotational symmetr…