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I want to learn combinatorics, and have read people's messages around here recommending Enumerative Combinatorics by Stanley; most of these suggestions also state that it's a dense book. If by dense they mean that it is really detailed, I have no problem with it, but it also makes me wonder if I need any previous knowledge before reading it.

Thanks in advance.

J W
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Daniel Bonilla Jaramillo
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    Plenty of "mathematical maturity". – Angina Seng Mar 30 '18 at 06:36
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    By the way, I highly recommend Bruce Sagan's new book called Combinatorics: The Art of Counting. A draft is freely available from the author's website here. The book is a gentle introduction (at the graduate level) to the field of enumerative combinatorics, and may be an easier read than Stanley's books. You may find it interesting to know that Sagan's PhD advisor was Stanley. – Prism May 26 '23 at 08:30

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I think "dense" might be meant in the sense of packing in a lot of mathematics per page. In one sense, this is "detailed" but in another it isn't, as readers may be expected to fill in or work out certain details themselves. Being comfortable with doing this is part of the mathematical maturity that Angina Seng mentions in the comment above.

If you're new to combinatorics, it might be wiser to first read one of the many excellent undergraduate combinatorics books out there or possibly a discrete mathematics book. See, for instance, the extensive list here.

As for prerequisites, starting from scratch would be tough going. A solid background in linear and abstract algebra, along with some complex analysis will help.

J W
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