Combinatorics: Solutions, Additions, Corrections

BOOK This page relates to the book Combinatorics: Topics, Techniques, Algorithms by Peter J. Cameron, Cambridge University Press, 1994 (reprinted 1996). The ISBN is
  • 0 521 45133 7 (hardback)
  • 0 521 45761 0 (paperback).
Bibliographical details are given here.

You can

Other links are provided too.

From the review by A. T. White in Zentralblatt für Mathematik:

I highly recommend this book to anyone with an interest in the topics, techniques, and/or algorithms of combinatorics.

Solutions to the exercises

The solutions are in PDF format: there is one file for each chapter. Only the first eleven chapters are available as yet (work in progress on the remainder), and detailed solutions to projects are not given.
  1. What is combinatorics?
  2. On numbers and counting
  3. Subsets, partitions, permutations
  4. Recurrence relations and generating functions
  5. The Principle of Inclusion and Exclusion
  6. Latin squares and SDRs
  7. Extremal set theory
  8. Steiner triple systems
  9. Finite geometry
  10. Ramsey's Theorem
  11. Graphs
Solutions to the remaining exercises are in preparation.

From the book

Here are LaTeX picture files for some of the diagrams in the book:

Further topics

This section will grow! I hope to outline such things as a proof of Dilworth's Theorem from Hall's (p. 196); Schnyder's Theorem, that a graph is planar if and only if its incidence poset has dimension at most 3 (p. 207); Wilf's inclusion-exclusion formula for the chromatic polynomial of a graph.

There are many interesting links between several of the topics mentioned in the book: graph colourings (p. 294), trees and forests (p. 162), matroids (p. 203), finite geometries (chapter 9), and codes (chapter 17, especially Section 17.7). Here is a short article describing some of these links, in PDF format.

Here are some curiosities about Fibonacci numbers, which are not as well known as they deserve to be, based on a conversation with John Conway. You can also learn more about Fibonacci numbers and related things at the Fibonacci pages at the University of Surrey.

Here is a proof of the Erdös-Ko-Rado theorem.


A collection of exercises is in preparation.

I have an idiosyncratic collection of research problems, with comments on the current state of knowledge, in my problem list. See especially problems 6, 12 and 18 in this list.

Further references

An update of the list of references: Check the file containing further quotations related to combinatorics.

Other links

Some links mentioned in the book are The Sequence Finder is now available as a Website.

Other links of interest:

Links to the author and publisher are at the head of this page.

Email the author or the artist from here!

Page maintained byPeter J. Cameron
26 March 2002.