5:52 AM
3

I was curious about the diagrammatic magic of @YaakovBaruch's recent comment, and so clicked on the relevant diagram and viewed its TeX source. This source turned out to use a macro \x which, I assume, was defined earlier in the comment. In this case, I think that I can find the definitions in t...

Prior comment clarified: any invariant must separate the 2 cases \quad\newcommand{\x}{\large\blacksquare}\begin{align}\x\\[-5pt]\x\\[-5pt]\x\end{align}\,\cup\, \big\uparrow\begin{align}&\x\x\x\x\x\x\x\x\x\\[-5pt]&\x\x\x\x\x\x\x\x\x\end{align}\big\uparrow\,\cup\, \big\uparrow\begin{align}&\,\,\longrightarrow\\[-5pt]&\x\x\x\\[-5pt]&\x\x\x\\[-5pt]&\x\x\x\\[-5pt]&\,\,\longrightarrow\end{align}\big\uparrow\quad and \quad\begin{align}&\x\x\x\x\x\x\x\x\x\x\\[-5pt]&\x\x\x\x\x\x\x\x\x\x\\[-5pt]&\x\x\x\x\x\x\x\x\x\x \end{align},\quad since the 1st can be tiled with different numbers of L-shapes. — Yaakov Baruch 11 hours ago
@LSpice When I use "Show Math As/TeX Commands" on the first diagram, this is what I get: \quad\newcommand{\x}{\large\blacksquare}\begin{align}\x\\[-5pt]\x\\[-5pt]\x\end{align}\,\cup\,.
Naturally, he doesn't put newcommand again in the other formulas - it is enough to define the macro once.
Do you get something else for the first formula?

6:21 AM
In Chrome on Windows I see the newcommand - I pasted above what I see.
Of course, I have to view the source of the first diagram.
2

As mentioned in the comments, what appears to be happening is that macro definitions are stripped out when you ask your browser to display the Latex commands for some math you've highlighted (on chrome on mac, this is done by highlighting, right-clicking and selecting Show Math As -> Tex Commands...

Sorry, I meant to write "strips macros" rather than "scripts macros".

6:55 AM
@MartinSleziak I do see that. When I tried, I thought it was just two environments; I tried on what appeared to be the "first" math environment (which I now actually see was the second of four).
But, just to be clear, although my motivation was this specific comment, I could also find the definition in the parent post, so the specific source here was not what I was after in my MMO question (but thank you anyway for posting it!).

Ok, I am glad this was clarified.
@LSpice Actually, I wrote my answer mainly as a general answer on "How to get source of a comment (including MathJax/LaTeX)?"
At least that's what I tried to do.
Actually, I looked at the comment in question only after the first version of my answer was posted.
I am not sure whether this could be useful - I have added a CW answer with a few comment. (For testing.)
On Mathematics Meta there is a question about this from 2011 and there are several other questions on the same topic.
I guess this tells something about the comparison of the two sites that this came up on MO only in 2022. (Although probably there are many different possible interpretations.)

7:16 AM
@LSpice BTW I have added - since the question seems to me more like (support) than (discussion). Of course, it might be useful to leave , too. Since only such question can get into the - so this improve the chances that people will view this question.

7:57 AM

8 hours later…
3:54 PM
7

To answer your question about interesting combinatorial objects: Your Sylvester-Hadamard matrix example generalizes in at least two ways. The incidence matrix of any balanced incomplete block design or, more generally, $t$-design has constant row and column sums. Specifically, a BIBD\$(v,b,r,k,\...

Here is at least a Wayback Machine snapshot of the difference sets repository linked in the answer. I am not sure what would be good replacement for that dead link - it seems that D. Gordon has some database with this topic. — Martin Sleziak 16 mins ago
@MartinSleziak If I'm not mistaken, the old La Jolla Difference Set Repository was also Dan Gordon's work. I would guess the database you link to is the successor of that one. It seems less browsable than the old version, although I must admit it's been years since I used it, so I may be misremembering. The slides here, starting on page 9, show how to enter search terms to generate various tables. — Will Orrick 2 mins ago
> Added 12 July 2022: I just updated the link above to the La Jolla Difference Set Repository, which is now the La Jolla Combinatorics Repository. Dan Gordon's slides here have examples showing how to query the database.