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I have to design a hoodie for my computer science batch, and I want it to be related to Theoretical computer science. I don't want to slap on some text with HTML-like angle brackets, but actually want something cool + nerdy that only people with some basic knowledge of CS might understand. I would be grateful, if you could give some suggestion, resources for ideas, or links to similar products. Thank you.

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I've always found this tattoo pretty daring. Would work on a hoodie.

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  • $\begingroup$ This answer could be much improved if it included more than just a link. $\endgroup$ Nov 24 at 0:56
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As an undergraduate student, I was a bit mystified by the occurrence of the notion of entropy (from physics) into theoretical computer science (at the time, for the description of the optimal compression of a text with $n_i$ occurrences (summing to $n=\sum_{i\in[1..k]}n_i$) of each symbol $i\in[1..k]$ by prefix free codes, such as the one described by David A. Huffman) and its (at the time to me) occult definition: $${\cal H}(n_1,\ldots,n_k) = \sum_{i\in[1..k]} \frac{n_i}{n} \log_2\frac{n}{n_i}.$$ Since then, I have learned to respect its potency and adequacy in measuring the (des)equilibrium of probability and frequency distributions, and I have used it to measure the spaced used by compressed data structures, the time used by adaptive algorithms (in internal and external memory), sometimes in convoluted ways, and even in instance optimality results.

Entropy Formula in Theoretical Computer Science

In 2013, for a colleague's birthday anniversary, I drew quickly a feminine character holding an equation often used in our research, one of the definition of the entropy of a vector of integers. At the time I wrote on my blog "I hope that he will hang it in his office so that it helps his students to memorize it!", and a few years later, a PhD student admitted that he searched on the web for the blog post to find back the formula :).

The definition of the entropy that I used in this drawing, $$n{\cal H}(n_1,\ldots,n_k) = n\log_2 n - \sum_{i\in[1..k]} n_i \log_2 n_i,$$ is a bit atypical (one typically normalizes both sides of the equation by $n$, and combines the two $\log$ terms into one, maybe so that to make it closer to the definition used by statistical physicists). I like this formulation better because it highlights the terms measuring the imbalance of the distribution, and give an intuition into the various analysis which lead to such a formula.

Feel free to use either the formula itself or the drawing: I would be honored! (Do let me know if you do!)

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