Gauss-Lintel, an Algorithm Suite for Exploring Chord Diagrams

Abstract

Gauss diagrams, or more generally chord diagrams are a well-established tool in the study of topology of knots and of planar curves. In this paper we present a system description of Gauss-lintel, our implementation in SWI-Prolog of a suite of algorithms for exploring chord diagrams. Gauss-lintel employs a datatype which we call “lintel”, which is a list representation of an odd-even matching for the set of integers [0,..,2n–1], for efficiently generating Gauss diagrams and testing their properties, including one important property called realizability. We report on extensive experiments in generation and enumeration of various classes of Gauss diagrams, as well as on experimental testing of several published descriptions of realizability.