there is an evident general encoding of hyperbolic tesselations by round chord diagrams.

Is this made explicit anywhere?

In particular, I am wondering about the following:

It should be possible to obtain the round chord diagram for an $\{n,k\}$ tesselation at some finite stage by starting with a suitable horizontal chord diagram on $n-1$ strands, then iteratively “cabling” it into itself and forming vertical composites of that with itself, and finally taking the trace to a round chord diagram with a cyclic permutation.

Is this described anywhere?

]]>added pointer to these two, which might be close to the earliest appearance of the concept of chord diagrams (?):

Paul R. Stein,

*On a class of linked diagrams, I. Enumeration*, Elsevier Journal of Combinatorial Theory, Series A Volume 24, Issue 3, May 1978, Pages 357-366 (doi:10.1016/0097-3165(78)90065-1)Paul R. Stein, C. J. Everett,

*On a class of linked diagrams II. asymptotics*, Discrete Mathematics Volume 21, Issue 3, 1978, Pages 309-318 (doi:10.1016/0012-365X(78)90162-0)

added pointer to today’s

- Ali Assem Mahmoud, Karen Yeats,
*Connected Chord Diagrams and the Combinatorics of Asymptotic Expansions*(arXiv:2010.06550)

added pointer to today’s

- Noboru Ito,
*Based chord diagrams of spherical curves*(arXiv:2004.12121)

made explicit the definition of $\mathcal{A}^c$ (here)

]]>I have replaced the graphics illustrating a typical chord diagram (first graphics in the entry) with a new one (here) that may be a little more informative

]]>In a new Properties section *Relation to Chern-Simns diagrams* I added pointer to *chord diagrams modulo 4T are Chern-Simons diagrams modulo STU*.

No other text yet. To be expanded. But not tonight.

]]>added these pointers:

Discussion of chord diagrams encoding SYK model correlators as representing hyperbolic/holographic content:

{#BINT18} Micha Berkooz, Mikhail Isachenkov, Vladimir Narovlansky, Genis Torrents, Section 5 of:

*Towards a full solution of the large $N$ double-scaled SYK model*, JHEP 03 (2019) 079 (arxiv:1811.02584){#Narovlansky19} Vladimir Narovlansky, Slide 23 (of 28) of:

*Towards a Solution of Large $N$ Double-Scaled SYK*, Nazareth 2019 (pdf, NarovlanskySYK19.pdf:file)

following

- Micha Berkooz, Prithvi Narayan, Joan Simón,
*Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction*, JHEP 08 (2018) 192 (arxiv:1806.04380)

Fixed the diagrams now, hopefully. [Edit: there is something strange going on which causes the diagrams not to render correctly after an edit, but to render correctly after I re-render manually. I will look into it when I get the chance, probably this evening.]

]]>I created a short page for chord diagram, and also added a bit of relevant information to Vassiliev invariant.

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