Combinatorics of Finite Sets (Dover Books on Mathematics) [Paperback]

Ian Anderson (Author)

Book Description

Series: Dover Books on Mathematics | Publication Date: November 2, 2011

Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed.

Product Details

• Paperback: 272 pages
• Publisher: Dover Publications (November 2, 2011)
• Language: English
• ISBN-10: 0486422577
• ISBN-13: 978-0486422572
• Product Dimensions: 8.4 x 5.4 x 0.6 inches
• Shipping Weight: 9.9 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,640,953 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

36 of 36 people found the following review helpful:

5.0 out of 5 stars An excellent and unique perspective on combinatorics, November 8, 2003

By 

Todd Ebert (Long Beach California) - See all my reviews

This review is from: Combinatorics of Finite Sets (Dover Books on Mathematics) (Paperback)

When one thinks of combinatorics of finite sets, he or she might first think of codes and designs. But this book introduced me to an area of combinatorics which I knew very little about, namely extremal set problems and their solutions which fall under famous Theorems by famous mathematicians: Erdos-Ko-Rado, Sperner, and Kruskal-Katona to name a few. I found these topics fascinating and fun to think about, which is in large part due to the author's coherent style, organization, explanation, and expertise of the subject-matter. Moreover, the author provided solutions to *every* one of the 150+ problems!!! How many math books can boast such a claim? Aside from may be a rough presentation of Lemma 4.3.2 the rest of the book is a masterpiece which I hope will gain more recognition within the next twenty years.

I highly recommend this book to both mathematicians and computer scientists. Although the book has very few "algorithms" in it, the thinking and reasoning about discrete structures (e.g. families of finite sets and multisets) will do wonders in developing the mind of a computer scientist, whether advanced or undergraduate. Yet it is quite sad that many cs departments (and math for that matter) invest little if any curriculum in discrete mathematics. Hopefully this will change at least to the point where the cs major will take two or three semesters of discrete math instead of two or three of calculus. For, as this book demonstrates, calculus is not a prerequisite for engaging one's mind in some quite fascinating mathematical problems related to finite sets.

Finally, it should be noted that Bela Bollobas also has an interesting book titled "Combinatorics: Set Systems, etc...." which significantly intersects with this book, but not to the degree where the reader should think they are interchangeable. I recommend both, and to read Anderson's book first; as I believe this book lays a better foundation than the latter.

3 of 3 people found the following review helpful:

5.0 out of 5 stars certainly better than decent, October 18, 2007

By 

? guy - See all my reviews

This review is from: Combinatorics of Finite Sets (Dover Books on Mathematics) (Paperback)

This book provides excellent coverage of sperners theorem including multiple proofs ,like the original one by sperner and more concise proofs using closely related concepts. The various proofs of sperners theorem provides a firm understanding of its connections with many other fundamental topics in finite combinatorial mathematics.Great book for those that have a good grasp on algebraic concepts.