by Gian-Carlo Rota
Number of pages: 414
In 1998, Gian-Carlo Rota gave his famous course, Combinatorial Theory, at MIT for the last time. John N. Guidi taped the lectures and took notes which he then wrote up in an almost verbatim manner conveying the substance and some of the atmosphere of the course. Topics covered included sets, relations, enumeration, order, matching, matroids, and geometric probability.
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by Albert Nijenhuis, Herbert S. Wilf - Academic Press Inc
This is a collection of mathematical algorithms with many new and interesting examples in this second edition. The authors tried to place in the reader's hands a kit of building blocks with which the reader can construct more elaborate structures.
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This introduction to combinatorics, the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. Some ability to construct proofs is assumed.
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The main goal of this survey is to state clearly and concisely some of the most useful tools in algebraic and geometric enumeration, and to give many examples that quickly and concretely illustrate how to put these tools to use.
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Contents: Permutations; Combinatorial maps; The correspondence between combinatorial maps and graphs on surfaces; Map's mirror reflection and dual map; Multiplication of combinatorial maps; Normalized combinatorial maps; Geometrical interpretation...