Combinatorics: Solutions, Additions, Corrections
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.
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.
- What is combinatorics?
- On numbers and counting
- Subsets, partitions, permutations
- Recurrence relations and generating functions
- The Principle of Inclusion and Exclusion
- Latin squares and SDRs
- Extremal set theory
- Steiner triple systems
- Finite geometry
- Ramsey's Theorem
- 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:
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:
- L. W. Beineke and R. J. Wilson (editors), Graph
Connections: Relations between graph theory and other parts
of mathematics, Oxford University Press, 1997.
- R. L. Graham and J. Nesetril (editors), The Mathematics
of Paul Erdös, (2 volumes), Springer, Berlin, 1997.
- R. C. Read and R. J. Wilson, An Atlas of Graphs,
Oxford University Press, 1998.
Check the file containing further quotations
related to combinatorics.
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.