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.

Young\'s lattice - Wikipedia, the free encyclopedia

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Costas array - Wikipedia, the free encyclopedia

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probability - Rigorous nature of combinatorics - Mathematics Stack Exchange

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Combinatorial auction - Wikipedia

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File:Derangement4.png - Wikimedia Commons

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Connections between topology and combinatorics - Mathematics Stack Exchange

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Possible number of open sets in a topology - Mathematics Stack Exchange

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Heaps\' law - Wikipedia

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Assembly theory - Wikipedia

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Union-closed sets conjecture - Wikipedia

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DesignTheory.org (theoretical, computational, and statistical aspects of combinatorial designs)

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