# This week: going back to my dissertation and extending

edited September 2021

My dissertation developed a method of specifying the complexity of finite automorphisms (functions from a set to itself). I'd like to extend this to relations (i.e., no restriction that a single arrow departs a particular domain element).

Working with math in my zettelkasten has been interesting. The only difficulty has been with diagrams etc. I've found that working mainly physically and scanning the images and cleaning the text digitally has been a nice process without much overhead.

Proofs and particularly the elements of subproofs are natural since linking can double as both relation and implication; likewise examination of backlinks can be useful for examining assumptions / presuppositions.

In summary, its working reasonably well, I just need to work physically first, then transfer to digital.

Any shared experiences re mathematics research in your zettelkasten would be great.

For anyone with a combinatorial or number-theoretic bent, here is a newly discovered sequence of numbers generated by the main algorithm of my paper at the encyclopedia of integer sequences. https://oeis.org/A335725

• A new discussion about any shared experiences re mathematics research in your zettelkasten starts here.

• edited October 2021

Very interesting sequence. > @bradfordfournier said:

For anyone with a combinatorial or number-theoretic bent, here is a newly discovered sequence of numbers generated by the main algorithm of my paper at the encyclopedia of integer sequences. https://oeis.org/A335725

Very interesting sequence--I'll look at this more closely when I have more time. My submission to the OEIS from 2000 is https://oeis.org/A028498. Thanks for reminding me about the OEIS, incidentally.

Sean A. Irvine from New Zealand has been independently verifying the sequences of the OEIS and added some additional terms beyond the terms I contributed in 2000, with his starting at 234753130435824000, according to the history. So at least the sequence survived peer review twice.

Post edited by ZettelDistraction on

GitHub. Erdős #2. CC BY-SA 4.0. Problems worthy of attack / prove their worth by hitting back. -- Piet Hein.

• edited October 2021

I meant to write that the first thing I thought when I saw $(\sigma_{i,j}=\left|f^{-j}(i)\right|)$ (conjugating the finite domain $(X)$ of the self-map $(f:X\rightarrow X)$ to $([n]=\lbrace1,\ldots,n\rbrace)$): "Great idea. I wish I had thought of that."