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I have a math Ph.D. but my knowledge of combinatorics sucks and I simply don't know how to compute anything more complicated, i.e. what happens when we put restrictions on the allowed configurations etc.

What I'm working on currently seems to require increasing sophistication in combinatorics (complicated word problems etc.). Can anyone recommend any nice starting points. I don't mind compact rigorous books, but they should give a broad enough overview and not focus on just a few things.

vtt
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    I assume you're familiar with Concrete Mathematics? – tomasz May 10 '13 at 22:31
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    What is a complicated word problem? Maybe if you gave an example of what you have in mind we can refer you to an appropriate book. Combinatorics is an immense subject... – Mariano Suárez-Álvarez May 10 '13 at 22:35
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    This question is vague to an almost infuriating degree, especially coming from someone with a PhD in mathematics (weren't you taught to be pedantically precise to a fault like the rest of us?). Restrictions on the allowed configurations of what? You're not just asking for an introductory level combinatorics text, are you? – Pete L. Clark May 10 '13 at 23:27
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    Does this answer your question? Good Book On Combinatorics –  Jul 18 '21 at 20:26

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No clue what your working on, so I won't attempt to say what's suitable for whatever it is you're trying to learn. But your subject line is interesting. Here are some titles:

  • Enumerative Combinatorics, volumes I and II, by Richard Stanley
  • Combinatorial Identities, by John Riordan
  • Introduction to Combinatorial Analysis, by John Riordan
  • Generatingfunctionology, by Herbert Wilf
  • Advanced Combinatorics, by L. Comtet
  • Concrete Mathematics, by Donald Knuth

These are only a few things that come to mind right away . . . . . . .

Michael Hardy
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It depends on how sophisticated the problem is. Some problems are extremely difficult, and perhaps even currently impossible. Some advanced techniques are described in http://www.math.upenn.edu/~wilf/gfology2.pdf

Michael H
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Proofs that Really Count, by Benjamin and Quinn is great for self study.

Fred Daniel Kline
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