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2016•Journal of Knot Theory and Its RamificationsOpen access

Untangling trigonal diagrams

Erwan Brugallé, Pierre-Vincent Koseleff, Daniel Pecker

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Abstract

Let [Formula: see text] be a link of Conway’s normal form [Formula: see text], [Formula: see text], or [Formula: see text] with [Formula: see text], and let [Formula: see text] be a trigonal diagram of [Formula: see text] We show that it is possible to transform [Formula: see text] into an alternating trigonal diagram, so that all intermediate diagrams remain trigonal, and the number of crossings never increases.

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What this paper is about

Let [Formula: see text] be a link of Conway’s normal form [Formula: see text], [Formula: see text], or [Formula: see text] with [Formula: see text], and let [Formula: see text] be a trigonal diagram of [Formula: see text] We show that it is possible to transform [Formula: see text] into an alternating trigonal diagram, so that all intermediate diagrams remain trigonal, and the number of crossings never increases.

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Available abstract

Let [Formula: see text] be a link of Conway’s normal form [Formula: see text], [Formula: see text], or [Formula: see text] with [Formula: see text], and let [Formula: see text] be a trigonal diagram of [Formula: see text] We show that it is possible to transform [Formula: see text] into an alternating trigonal diagram, so that all intermediate diagrams remain trigonal, and the number of crossings never increases.

Key concepts: Trigonal crystal system, Diagram, Trigonal pyramidal molecular geometry, Crystallography, Link (geometry), Combinatorics, Physics, Chemistry

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