The elementary-transformation generation conjecture for chord diagrams

Consider the group of elementary transformations of chord diagrams that preserve their intersection graph. A share is a subdiagram used as a unit in the chord-diagram decompositions considered in the source.

Elementary-transformation generation conjecture. The group of elementary transformations is generated by transformations of the following two types: reflecting a share across another share, and turning a share upside down.

This conjecture seeks a general description of all transformations preserving an intersection graph and is presented as a first step toward determining the corresponding transformation group. The source does not resolve whether these two types generate the full group.