This is a wonderful little book about a very simple mathematical object known as the "integer partition". The concept is simple: a partition of a positive integer is the set of positive integers that when summed give that number. (i.e. one integer partition of 6 is [5, 1] another is [3, 2, 1]). Order is unimportant so [5,1] and [1,5] are the same partition.



Amazingly this simple idea gives rise to many rich investigations that are the basis for this book. Many of these relate to "counting" the number of partitions with a given property and relating the number of partitions with various properties to one another. In fact, the mere counting of the number of partitions of a large integer, like 200, requires a foray into generating functions, an extremely important area of combinatorics. The formal properties of integer partitions have been investigated for over 200 years by some of the brightest lights in the mathematical constellation, such as Euler and Ramanujan. One of the authors (Andrews) is probably the current leading expert in this field.



Using integer partitions as a starting point the authors take the reader into many areas of mathematics (for example, generating functions, bijective proofs, Ferrers graphs and partially ordered sets). Each chapter also provides a selection of graded exercises ranging from the simple to problems that in some cases would be considered research areas. An outline of the answers to problems is provided in the back of the book. Working the problems will certainly give your powers of reasoning a real workout.



I am not particularly skilled at mathematics, however, I found the discussion relatively easy to follow although most topics require serious study if a full understanding is to be had. I would think that this book would certainly appeal to the math hobbyist, but could easily be the basis for a semester seminar for the advanced undergraduate.



Five stars for this gem!

Скачать книгу бесплатно (djvu, 1.25 Mb)

---

Читать «Integer Partitions»