Virtually symmetric representations and marked Gauss diagrams

Symmetric Gauss - Lobattoand Modified Anti - Gauss Rules

Gauss Diagrams of 3-manifolds

The paper presents a simple combinatorial method to encode 3-dimensional manifolds, basing on their Heegaard diagrams. The notion of a Gauss diagram of a 3-manifold is introduced. We check the conditions for a Gauss diagram to represent a closed manifold and a manifold with boundary.

Chord Diagrams and Gauss Codes for Graphs

Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general graphs have not been studied, and are potentially equally valuable in the study of spatial graphs. We will define chord diagrams for planar embeddings of pl...

Mental Representations of Diagrams, Views about Diagrams, and Problem Solving

This study investigated people’s mental representations of diagrams and whether these related to views about diagrams and problem solving performance. The participants were 93 undergraduate students who were asked to complete a questionnaire which included free writing on the topic of diagrams, and problem solving. Analysis of the statements and ideas that the students wrote revealed four categ...

Diagrams for Symmetric Product Orbifolds

We develop a diagrammatic language for symmetric product orbifolds of two-dimensional conformal field theories. Correlation functions of twist operators are written as sums of diagrams: each diagram corresponds to a branched covering map from a surface where the fields are single-valued to the base sphere where twist operators are inserted. This diagrammatic language facilitates the study of th...