MathOverflow

(Most of the code and ideas in this post are from Discord user giantimp1, but this writeup is my own.)
Motivating idea
We call a natural number a "super-square in base $B$" if all substrings of its base-$B$ representation are squares. (The name is coincidentally reminiscent of Henri Picciotto's "super-slimes" for numbers whose base-$10$ substrings are all primes.)...

Let $G$ be a finite symmetric group, and let $\widehat G$ denote the set of (equivalence classes of) irreducible unitary representations of $G$. For $\rho\in\widehat G$ write $d_\rho$ for its dimension and realize $\rho:G\to\mathrm{U}(d_\rho)$. The tensor...

Say that a topological space $X$ is locally connected at some point $x$, if it has a local base at that point consisting of connected open sets.Also $X$ is locally connected if it is locally connected at each of its points.
It is well known that a connected space is not necessarily locally connected....

Consider the set of odd partitions of n. As n grows, what is the proportion which have at least as many parts of size 1 as distinct parts?
I'm not a combinatorialist, but this seems potentially within the wheelhouse of the right people(?).