# Book recommendation for Integer partitions and q series

I have been studying number theory for a little while now, and I would like to learn about integer partitions and q series, but I have never studied anything in the field of combinatorics, so are there any prerequisites or things I should be familiar with before I try to study the latter?

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Could you make the title more specific? –  Rahul Jan 21 '13 at 4:27

For a more difficult introduction to some of the real magic of $q$-series, try "Number Theory in the Spirit of Ramanujan" by Bruce C. Berndt.

Even if you don't understand the proofs (my condition for much of it), the theorems are amazing.

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I recently came across the book How to count: An introduction to Combinatorics. It is an excellent book to learn combinatorics through self study from scratch. It has lots of solved problems and applications discussed in a very nice manner. Plus it has two chapters on partitions so that you can get an introduction to partition theory too. You can then move on to George Andrews.

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You should look into "Additive combinatorics" by Terence Tao. It establishes the connection between the two.

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George Andrews has contributed greatly to the study of integer partitions. (The link with his name will take you to his webpage listing publications, some of which are accessible as pdf documents.) Also see, e.g., his classic text The Theory of Partitions and the more recent Integer Partitions.

You can pretty much "jump right in" with the following, though their breadth of coverage may be more than you care to explore (in which case, they each have fine sections on the topics of interest to you, with ample references for more in depth study of each topic):

Two books I highly recommend are

Concrete Mathematics by Graham, Knuth, and Patashnik.

Combinatorics: Topics, Techniques, and Algorithms by Peter J. Cameron. See his associated site for the text.

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George Andrews and Kimmo Eriksson, Integer Partitions, is a very nice book about the topics you want to learn about. It says it requires nothing more of the reader "than some familiarity with polynomials and infinite series".

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I second this strongly, it's a lovely book. –  Chris Godsil Jan 18 '13 at 2:36
A great book I have used several times in upper division undergraduate seminar courses. –  Brian Hopkins Jan 23 '13 at 4:12