RFE Nov 2025: Disk domain wall degeneracies for branes I and II

[Sean A. Irvine]

Hi,

I am very pleased with how the previous two months' requests for enhancement have led to substantial improvements in two blocks of sequences.

This month I would like to draw attention to another block of sequences, this time with what sounds like (at least to me) a mathematical physics flavor.

Provide explanations, formulas and/or programs for the sequences from A061605 to A061637. All of these sequences are based on a paper by Aganagic, Klemm, and Vafa (available via the Link in the corresponding sequences), but the corresponding OEIS sequences are currently lacking in details.

I track these questions here:

https://oeis.org/wiki/User:Sean_A._Irvine/Requests_for_Enhancements#Requests_for_Enhancements

Sean.

[Alex Violette]

Hi Sean,
I did a quick look at all those sequences and it appears all but one of them(A061628) should have the keyword more(unless someone finds enough terms for one or more of those sequences quickly). That, and I'm curious why A061605-A061627 alongside A061628-A061637 all share the same title.

Regards,
Alex Violette

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[Tom Duff]

It looks like these are all individual rows of several 2-dimensional arrays and the row numbers are not recorded. OEIS should probably have entries for the 2d tables (are they there already?) and these sequences should refer to them.

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[Tom Duff]

Looks like the tables are actually 3-dimensional. I don't even know how those are canonically represented in the OEIS.

[Andrei Zabolotskii]

Two things about these sequences:

1. When the Aganagic, Klemm & Vafa paper seem to contain less terms than the OEIS, the missing term(s) actually can be found in the TeX source of the preprint that can be downloaded from arXiv.

2. Some of these sequences arise as diagonals (sic) in tables from some other paper such as the papers by Mayr and by Alim et al., referenced in A061628 (found by searching the terms in Google Scholar). Sometimes they have more terms. I don't remember whether it was obvious that these are really the same sequences. Perhaps I only extended one sequence from these other papers because it wasn't obvious at all.

Andrei

воскресенье, 2 ноября 2025 г. в 22:18:39 UTC, eigenv...@gmail.com:

[M F Hasler]

I think the NAMEs could be prefixed with "Ooguri-Vafa invariants of ...", 

which gives a little more lead but is still an unsatisfying definition.

But it might not be easy to find a good name, since in the two papers  (Aganagic et al. vs Alim et al.)

they are presented, denoted and listed differently.

(In one of the two they are rows, in the other one they are diagonals in some tables.

But I think the second, with notation N_beta = N_(k, m, l), is closer to the original paper from  Ooguri and Vafa,

Nucl.Phys.B577:419-438,2000 and arXiv:hep-th/9912123

Question: should we leave kw "obsc" and/or rather a comment "Needs a better description" until a really satisfying definition is given?

 - Maximilian

[Sean A. Irvine]

Just discovered there is yet a further block of related sequences, similarly lacking detail:

A092698 through A092726 all with the name "Disk degeneracies for brane III in the O(K)->P^1 x P^1 geometry."

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