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A Course in Combinatorics
About this book
This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.
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Yes, you can access A Course in Combinatorics by J. H. van Lint,R. M. Wilson in PDF and/or ePUB format, as well as other popular books in Mathematics & Discrete Mathematics. We have over one million books available in our catalogue for you to explore.
Information
1.
Graphs
3
in
both
graphs
(using
1
,
2
,
3
,
4
,
5
,
6)
and
observe
that
the
edge
sets
are
the
same
sets
of
unordered
pairs.
Figure
1.3
A
permutation
Ï
of
the
vertex
set
of
a
graph
G
with
the
property
that
{
a,
b
}
is
an
edge
if
and
only
if
{
Ï
(
a
)
,
Ï
(
b
)
}
is
an
edge,
is
called
an
automorphism
of
G
.
Problem
1A.
(i)
Show
that
the
drawings
in
Fig.
1.4
represent
the
same
graph
(or
isomorphic
graphs).
(ii)
Find
the
group
of
automorphisms
of
the
graph
in
Fig.
1.4.
Remark:
There
is
no
quick
or
easy
way
to
do
this
unless
you
are
lucky;
you
will
have
to
experiment
and
try
things.
Figure
1.4
The
complete
graph
K
n
on
n
vertices
is
the
simple
graph
that
has
all
(
n
2
)
possible
edges.
Two
vertices
a
and
b
of
a
graph
G
are
called
adjacent
if
they
are
distinct
and
joined
by
an
edge.
We
will
use
Î(
x
)
to
denote
the
set
of
all
vertices
adjacent
to
a
given
vertex
x
;
these
vertices
are
also
called
the
neighbors
of
x
.
Table of contents
- Cover
- Title Page
- Copyright
- Contents
- Preface to the first edition
- Preface to the second edition
- 1. Graphs
- 2. Trees
- 3. Colorings of graphs and Ramseyâs theorem
- 4. TurĂĄnâs theorem and extremal graphs
- 5. Systems of distinct representatives
- 6. Dilworthâs theorem and extremal set theory
- 7. Flows in networks
- 8. De Bruijn sequences
- 9. Two (0, 1, *) problems: addressing for graphs and a hash-coding scheme
- 10. The principle of inclusion and exclusion; inversion formulae
- 11. Permanents
- 12. The Van der Waerden conjecture
- 13. Elementary counting; Stirling numbers
- 14. Recursions and generating functions
- 15. Partitions
- 16. (0, 1)-Matrices
- 17. Latin squares
- 18. Hadamard matrices, ReedâMuller codes
- 19. Designs
- 20. Codes and designs
- 21. Strongly regular graphs and partial geometries
- 22. Orthogonal Latin squares
- 23. Projective and combinatorial geometries
- 24. Gaussian numbers and q-analogues
- 25. Lattices and Möbius inversion
- 26. Combinatorial designs and projective geometries
- 27. Difference sets and automorphisms
- 28. Difference sets and the group ring
- 29. Codes and symmetric designs
- 30. Association schemes
- 31. (More) algebraic techniques in graph theory
- 32. Graphconnectivity
- 33. Planarity and coloring
- 34. Whitney Duality
- 35. Embeddings of graphs on surfaces
- 36. Electrical networks and squared squares
- 37. PĂłlya theory of counting
- 38. Baranyaiâs theorem
- Appendix 1. Hints and comments on problems
- Appendix 2. Formal power series
- Name Index
- Subject Index