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aigner m combinatorial theory 1979

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Textbook in PDF format The present book covers most aspects of parts (a) and (b), but none of (c). The reasons for excluding (c) were twofold. First, there exist several older books on the subject, such as Ryser [1] (which I still think is the most seductive introduction to combinatorics), Hall [2], and more recent ones such as Cameron-Van Lint [1] on groups and designs, and Blake-Mullin [I] on coding theory, whereas no comprehensive book exists on (a) and (b). Second, the vast diversity of types of designs, the very complicated methods usually still needed to prove existence or non-existence, and, in general, the rapid change this subject is presently undergoing do not favor a thorough treatment at this moment. I have also omitted reference to algorithms of any kind because I feel that presently nothing more can be said in book form about this subject beyond Knuth [1], Lawler [1], and Nijenhuis-Wilf[l]. As to the second point, that of systematizing the definitions, methods, and results into something resembling a theory, the present book tries to accomplish just this, admittedly at the expense of some of the spontaneity and ingenuity that makes combinatorics so appealing to mathematicians and non-mathematicians alike. To start with, mappings are grouped together into classes by placing various restrictions on them. To stick to the division outlined above, these classes of mappings are then counted, ordered, and arranged. The emphasis on ordering is well justified by the everyday experience of a combinatorist that most discrete structures, while perhaps lacking a simple algebraic structure, invariably admit a natural ordering. Following this program, the book is divided into three parts, the first part presenting the basic material on mappings and posets, in Chapters I and II, respectively, the second part dealing with enumeration in Chapters III to V, and the third part on the order-theoretical aspects in Chapters VI-VIII

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aigner m combinatorial theory 1979

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