Combinatorics may very loosely be described as that branch of
mathematics which is concerned with the problems of arranging objects in
accordance with various imposed constraints. It covers a wide range of
ideas and because of its fundamental nature it has applications
throughout mathematics. Among the well-established areas of
combinatorics may now be included the studies of graphs and networks,
block designs, games, transversals, and enumeration problem s concerning
permutations and combinations, from which the subject earned its title,
as weil as the theory of independence spaces (or matroids). Along this
broad front, various central themes link together the very diverse
ideas. The theme which we introduce in this book is that of the abstract
concept of independence. Here the reason for the abstraction is to
unify; and, as we sh all see, this unification pays off handsomely with
applications and illuminating sidelights in a wide variety of
combinatorial situations. The study of combinatorics in general, and
independence theory in particular, accounts for a considerable amount of
space in the mathematical journais. For the most part, however, the
books on abstract independence so far written are at an advanced level,
-whereas the purpose of our short book is to provide an elementary in-
troduction to the subject.
