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 -- 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.