These are some short notes on what I've doing these days.

Unfortunately, there isn't much to talk about. I think that one of the most relevant things that I did was to resurrect one of my best audio-extracting CD-ROM drives: just opened the case of my computer, took off the CD drive, opened, cleaned its lens, lubricated the moving parts and everything is back to normal operation.

This sense of "getting something for nothing" is hard to explain to those who have not experienced it already.

Other things that I did was to grab some old CDs that I had laying here (Radiohead's OK Computer, Pantera's Far Beyond Driven, the tribute to Queen called "Dragon Attack", and Gentle Giant's Free Hand, among others). Dream Theater's Special Edition of Systematic Chaos is quite good, but unfortunately I don't have a 5.1 system at my disposal.

I also selected some material for further studies. I'm right now studying group actions (or G-sets as some seem to prefer). Soon, I will be finishing the basics of Group Theory (hey, really, why is the Class Equation of groups that "famous"? It is just a matter of saying that \(|X| = \sum_{x\in X} 1\), but with cardinality of orbits instead of with one's and with a transversal of the orbits in place of \(X\) itself).

Actually, if the orbits of the elements of the \(G\)-set \(X\) consist of just one element, then the equation above is the Class Equation (what some people would call \(\mathop{\mathrm{Fix}}(X)\), I would call the "orbits being trivial").

Anyway, Burnside's lemma (which actually seems to be wrongly attributed, since it seems to be discovered independently by Cauchy and Frobenius) for counting orbits of a given action of a \(G\)-set has nice implications in combinatorics and it should be, at least, mentioned in any self-respecting introduction to Group Theory.

Oh, I almost forgot one of the major things that I did today (2007-06-12): I finally learned how to manipulate the quilt patch-system (initiated by Andrew Morton). The crucial point that is not written anywhere: the patches, by default, are applied with -p1 instead of -p0. This took me quite some time to get, as the documentation isn't explicit about it. Installation of quilt in a MacOS X system is not trivial, due to the demand of GNU tools.

But now I can keep some Debian packages of mine in a better shape than if I were just applying a single monolithic patch.

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