MathOverflow

I began my exploration with an observation - that even-vertex tilings can be systematically colored in such way as to generate new non-MLD companion tilings.
Formally, I expressed this in the following theorem:
Theorem: For any even-vertex aperiodic tileset $T$, where there exists a substitution rule S, the transformation $\Phi$ produces a companion aperiodic tileset $T'$.Trivial Outcome: The tile-transition graph is disjoint (reflecting a tile is a choice...

Improving bedroom decor on a budget is totally possible if you focus on small but impactful changes instead of a complete makeover.
Start with upgrading your bedsheets and cushions, as they instantly change the overall look of the room. Go for soft, modern designs that match your wall colors. Adding a simple rug, warm lighting, or a few decorative items like candles and wall art...

I have a puzzle on the explicit expression for the $\varepsilon$-factor $\varepsilon(f\otimes \chi,1/2)$ for the twisted L-function $L( f\otimes \chi,s)$, where $\chi \bmod q$, a primitiveDirichlet character of modulus $q$, and $f\in S^*(q,\chi)$, a...

Soft question!
I've been working on a general topology book that is often veering into the realm of a continuum theory book, where there are lots of big theorems that are hiding away in obscure papers. It's become a bit of sidequest to grab a lot of theorems not currently...