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The Unity of Combinatorics

Ezra Brown and Richard K. Guy
Publisher: 
AMS
Publication Date: 
2020
Number of Pages: 
353
Series: 
The Carus Mathematical Monographs
Price: 
65.00
ISBN: 
978-1-4704-5279-7
Category: 
Monograph
BLL Rating: 
BLL

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Miklós Bóna
, on
08/23/2020
]
Combinatorics is a vast field. The Mathematical Subject Classification of the American Mathematical Society divides it into five major and more than 50 minor subfields. It is, therefore, reasonable to ask what holds Combinatorics together?  What connects an argument in design theory to an argument in the combinatorics of partially ordered sets?
 
In this book, the authors set out to show that there are plentiful connections among remote-looking parts of combinatorics. For instance, Kirkman's schoolgirl problem and the (7,3,1)-design that it involves, are shown to be connected to Latin squares, normed algebras, field extensions, and, perhaps most surprisingly, matroids. 
 
Design theory has a leading role in the book, but we find excursions to combinatorial number theory, group theory, and geometry, as well as enumerative combinatorics and the theory of packings and tilings. 
 
The various chapters can be read fairly independently. The most frequent users of the book will probably be instructors who are looking for examples to illustrate the applicability of a subfield of combinatorics (particularly design theory) into the other. They will find plenty of examples of that kind, with their context well explained.
 
Miklós Bóna is a Professor and Distinguished Teaching Scholar at the University of Florida, and the author and editor of several books. His main research interest is Enumerative Combinatorics.

See the publisher's web page.

Tags: 
Combinatorics