# An Uncitable Result?

My colleague Pablo Soberon just showed me an unusually problematic result to cite, and I wanted to share this weird story. If you have other weird citation stories, do tell!

Yes, this is a second silly post in a row. Lately I’m not finding the time to write more serious ones. And the silly stories need to be documented somewhere…

This story begins with a Japanese anime show called The Melancholy of Haruhi Suzumiya. I don’t know much about this show, but apparently there are several different orders in which one can watch the episodes. This led a fan of the show to ask for the minimum number of episodes one needs to watch, so that you saw all the episodes in every possible order. In other words, the minimum sequence of the numbers from $\{1,\ldots,n\}$ that contains every possible permutation of the numbers. (if I understand correctly, each order has to appear consecutively, with no additional numbers in between). This was on 4chan in 2011. A solution was then offered by an anonymous user, and this disappeared among the other weird anime discussions around the web.

It turns out that some people have been studying the above question as a serious math problem, prior to the show and not aware of it. The sequence containing all of the possible permutations is referred to as a superpermutation. See for example here and here. One paper about this was even published in the journal “Discrete Mathematics” in 2013.

Now the people coming from the mathematical angle discovered the original 4chan discussion, and in it the solution to the problem. So can they cite this result? It is by an anonymous person and appeared on an anime fans website. If this is not complicated enough, the relevant website no longer exists. Instead, the original discussion was discovered on a site that archives old online discussions. And it’s unclear how stable this archive site is. Luckily, this is not my problem!

# Mathematical Energy: Etymology

This might be the silliest post I’ve written so far (yes – worse than “Was Disney trying to kill mathematicians?”). I urge you to stop reading now unless (i) you are quite familiar with the mathematical notion of energy (e.g., additive energy), and (ii) you have a horrible sense of humor.

The term energy was coined by Tao and Vu. I like “energy” as a name for this object, but I never had a good answer when asked why this is how it’s called. That is, until a referee report provided me with an answer. And this wonderful referee probably didn’t even know it.

In a recent paper, Cosmin Pohoata and I used “color energy”. We have a graph $G=(V,E)$ with colored edges. Denote the color of an edge $(v_1,v_2)$ as $\chi(v_1,v_2)$. The color energy of $G$ is

$E(G) = \left|\left\{(v_1,v_2,v_3,v_4)\in V^4 :\ \chi(v_1,v_2) = \chi(v_3,v_4) \right\}\right|.$

The referee complained about our notation for the multiplicity of a color $c$ (the number of edge of color $c$), and asked to change it to $m_c$. After this change of notation, the energy is defined by the standard formula

$E = \sum m_c^2.$