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A Primer in Combinatorics

Alexander Kheyfits
De Gruyter
Publication Date: 
Number of Pages: 
[Reviewed by
Manjil Saikia
, on
See our review of the first edition of this book.
The book under review covers almost all of the basics in a first course in combinatorics and graph theory, and much more. An interesting aspect of the book are two chapters (Chapters 3 and 6) on practical applications of combinatorics, which are not so explicitly written about in textbooks. A major change from the 1st edition of the book was the addition of Chapter 6, which in the opinion of the reviewer, immediately increases the value of this edition over the previous one.
The book is divided into two parts, the first part focuses on the basics of combinatorics and graph theory. This part is very well-written with lot of examples and exercises for the reader to get a very good grasp of the subject matter. The second part, called ‘Combinatory analysis’ focuses on more advanced topics such as generating functions, Ramsey theorem, block designs, etc. There were several missed opportunities in this part; for instance there could have been some more discussion on permutations which have several very interesting combinatorial problems attached to them, and maybe even posets and q-analogues could have been given some space. But such complaints will arise for any book of this scope which as the title suggests is a ‘primer’ and not a comprehensive introduction to the subject.
The first part of the book is intended for a first course in combinatorics and graph theory. The reviewer feels this aim of the book is well-achieved. However, the notion of the second part containing material for an entry-level graduate course in combinatorics as expressed by the author in the preface is not correct in the view of this reviewer. This would be more of a second course in combinatorics for undergraduates. It would have been more interesting to include some topics of current interest in algebraic combinatorics and analytic combinatorics to make the second part more attractive for advanced students. Notwithstanding these quibbles, the reviewer feels this is a well motivated book and would be a fine addition to the teaching repertoire of combinatorialists and graph theorists.


About the reviewer: Manjil Saikia ( is presently at Cardiff University, UK. He studied mathematics at Tezpur (India), Trieste (Italy) and Vienna (Austria), and manages the bilingual (Assamese and English) website Gonit Sora (