My study of chord diagrams is motivated by its relevance to statistical physics models. Most notably the SYK (Sachdev-Ye-Kitaev) model and the Parisi's hypercube model (arXiv:cond-mat/9410088). In both models it is the intersection structures of the chord diagrams that are essential.
The central theme is combinatorics, and these are mathematica codes (.nb files).
Some enumeration identities now have simple bijective proofs, by representation of words and degenerate words (see appendix C.2 of my doctoral thesis).