Along with statistics, combinatorics is one of the most maligned fields of mathematics. Often it is not even considered a field in its own right but merely a grab-bag of disparate tricks to be exploited by other, nobler endeavours. Where is the glory in simply counting things? This book goes a long way towards shattering these old stereotypes. By unifying enumerative combinatorics under a strong algebraic framework, Aigner finally bestows upon the humble act of counting the respect it so surely deserves.

At first, it may be somewhat trying to make sense of his presentation as he reworks familiar results in this algebraic view. Often, I was left wondering why it is necessary to go through the trouble of all these high-powered techniques just to obtain results we've already obtained through much simpler means. However, as I progressed through the chapters, it became clear that the only consistent way to tackle the truly difficult problems in enumeration was with these algebraic tools.

If you are serious about combinatorics or merely interested in what combinatorics has to offer, this volume is certainly a valuable addition to your library.

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