Commentary by cpressey on Combinatorics works ============================================= ### Introductory Combinatorics Looks interesting -- it's interesting how close combinatorics is to discrete math. ### Analytic Combinatorics Has a lot which is beyond me, but there's some good stuff in here. ### Introduction to Random Graphs Has a lot which is beyond me, but random graphs are obviously interesting and important, and it goes into a few applications and things. ### Boltzmann Samplers for the Random Generation of Combinatorial Structures When you are writing some _ad hoc_ code to generate a random structure -- for example, for a property test, or for [NaNoGenMo](https://github.com/NaNoGenMo/) -- there are two things you realize sooner or later: * If the resulting structure doesn't have the properties you want, you can throw it out and start over. * If the structure is recursive, you need to be careful about the probability of recursing; if it's too high, there is a tendency for your structures to grow indefinitely. The theory of Boltzmann Samplers formalizes these two things. ### What Lies Between Order and Chaos? Not technical -- a certain amount of philosophizing, popularizing, and reminiscing. ### The Math of Card Shuffling The page is written in Idyll, a markup format similar to Markdown for producing documents similar to Jupyter Notebooks. ### Young\'s lattice - Wikipedia, the free encyclopedia ### Costas array - Wikipedia, the free encyclopedia ### Rigorous nature of combinatorics ### Combinatorial auction - Wikipedia ### File:Derangement4.png - Wikimedia Commons ### Connections between topology and combinatorics ### Possible number of open sets in a topology ### Heaps\' law - Wikipedia ### Assembly theory - Wikipedia ### Union-closed sets conjecture - Wikipedia ### DesignTheory.org (theoretical, computational, and statistical aspects of combinatorial designs)